Udemy - Linear Algebra and Geometry 3

Creation Time	May 2, 2024, 9:50 p.m.
Last Access Time	Nov. 16, 2024, 6:20 a.m.
File Size	37.7 GB
Keywords	and Linear Algebra Geometry - Udemy 3
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Total Files	509
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3. More problem solving; spaces different from R^n/5. In the space of polynomials, Problem 5.mp4 965.4 MB
3. More problem solving; spaces different from R^n/1. Eigendecomposition, Problem 1.mp4 891.7 MB
3. More problem solving; spaces different from R^n/4. Powers and roots, Problem 4.mp4 768.3 MB
3. More problem solving; spaces different from R^n/2. Eigendecomposition, Problem 2.mp4 579.5 MB
2. Geometrical operators in the plane and in the 3-space/12. Spectral decomposition, Geometrical illustration, Problem 8.mp4 570.1 MB
7. Inner product as a generalization of dot product/14. Gram matrix, Problem 3.mp4 564.4 MB
2. Geometrical operators in the plane and in the 3-space/7. Problem 5 Projection in the 3-space.mp4 561.3 MB
9. Projections and Gram–Schmidt process in various inner product spaces/4. Orthonormal sets of continuous functions, Problem 1.mp4 558.7 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/9. More new facts about AT A six equivalent statements.mp4 536.6 MB
3. More problem solving; spaces different from R^n/7. In the space of matrices, Problem 7.mp4 507.7 MB
2. Geometrical operators in the plane and in the 3-space/6. Problem 4 Projection in the 3-space.mp4 499.6 MB
5. Recurrence relations, dynamical systems, Markov matrices/12. Steady-state vector (equilibrium vector), Problem 7.mp4 499.0 MB
3. More problem solving; spaces different from R^n/3. Powers and roots, Problem 3.mp4 489.1 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/9. Cauchy-Schwarz inequality, proof 1.mp4 448.0 MB
12. Quadratic forms and their classification/17. Quadratic surfaces, shortest distance, Problem 8.mp4 436.3 MB
11. Diagonalization of symmetric matrices/17. Pos and neg definite matrices, semidefinite and indefinite matrices, Problem 9.mp4 434.2 MB
11. Diagonalization of symmetric matrices/5. Eigenvalues for a (real) symmetric matrix are real.mp4 427.8 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/7. SVD, reduced singular value decomposition, Problem 1.mp4 423.5 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/6. Singular value decomposition with proof and geometric interpretation.mp4 422.1 MB
12. Quadratic forms and their classification/1. The correspondence between quadratic forms and symmetric matrices is 1-to-1.mp4 414.9 MB
4. Intermezzo isomorphic vector spaces/12. Vector spaces, fields, rings, Problem 5.mp4 413.1 MB
5. Recurrence relations, dynamical systems, Markov matrices/4. Systems of difference equations, Problem 1.mp4 412.4 MB
4. Intermezzo isomorphic vector spaces/4. A necessary condition for isomorphic vector spaces.mp4 405.7 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/10. Cauchy-Schwarz inequality, proof 2.mp4 400.0 MB
9. Projections and Gram–Schmidt process in various inner product spaces/13. Gram-Schmidt in IP spaces, Problem 7.mp4 397.9 MB
4. Intermezzo isomorphic vector spaces/11. Vector spaces, fields, rings, Problem 4.mp4 397.5 MB
6. Solving systems of linear ODE, and solving higher order ODE/10. Another way of looking at the same problem.mp4 393.3 MB
9. Projections and Gram–Schmidt process in various inner product spaces/9. Orthogonal projections on subspaces of an IP space, Problem 4.mp4 373.7 MB
11. Diagonalization of symmetric matrices/1. The link between symmetric matrices and quadratic forms, Problem 1.mp4 371.7 MB
5. Recurrence relations, dynamical systems, Markov matrices/5. Systems of difference equations, Problem 2.mp4 365.2 MB
7. Inner product as a generalization of dot product/13. Matrix inner products on R^n, Problem 2.mp4 363.9 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/5. ON-bases containing only eigenvectors of certain matrix products.mp4 357.5 MB
12. Quadratic forms and their classification/13. Different roles of symmetric matrices (back to Videos 150 and 168), Problem.mp4 355.1 MB
5. Recurrence relations, dynamical systems, Markov matrices/9. Higher order difference equations, Problem 6.mp4 350.3 MB
7. Inner product as a generalization of dot product/12. Quadratic forms and how to read them.mp4 347.8 MB
2. Geometrical operators in the plane and in the 3-space/5. Problem 3 Symmetry in the 3-space.mp4 347.4 MB
4. Intermezzo isomorphic vector spaces/9. Isomorphic spaces Problem 3.mp4 345.8 MB
10. Min-max problems, best approximations, and least squares/5. Min-max, Problem 4.mp4 344.7 MB
5. Recurrence relations, dynamical systems, Markov matrices/7. Higher order difference equations, Problem 4.mp4 341.2 MB
10. Min-max problems, best approximations, and least squares/6. Min-max, Problem 5.mp4 341.2 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/19. Triangle inequality in inner product spaces.mp4 341.0 MB
10. Min-max problems, best approximations, and least squares/2. Min-max, Problem 1.mp4 337.8 MB
11. Diagonalization of symmetric matrices/12. Orthogonal diagonalization, Problem 4.mp4 335.1 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/11. Pseudoinverse, Problem 3.mp4 333.0 MB
12. Quadratic forms and their classification/11. Classification of curves, Problem 4.mp4 328.2 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/23. Generalized Theorem of Pythagoras, Problem 10.mp4 315.8 MB
3. More problem solving; spaces different from R^n/6. In the space of polynomials, Problem 6.mp4 311.7 MB
5. Recurrence relations, dynamical systems, Markov matrices/15. Markov matrices, Problem 10, Election.mp4 297.8 MB
5. Recurrence relations, dynamical systems, Markov matrices/8. Higher order difference equations, Problem 5.mp4 296.6 MB
6. Solving systems of linear ODE, and solving higher order ODE/5. The method.mp4 292.8 MB
11. Diagonalization of symmetric matrices/14. Orthogonal diagonalization, Problem 6.mp4 287.8 MB
10. Min-max problems, best approximations, and least squares/19. Least squares straight line fit, Problem 12.mp4 285.9 MB
10. Min-max problems, best approximations, and least squares/17. Least squares, Problem 11, by normal equation.mp4 278.7 MB
12. Quadratic forms and their classification/19. Quadratic surfaces, Problem 10.mp4 277.2 MB
9. Projections and Gram–Schmidt process in various inner product spaces/10. Orthogonal projections on subspaces of an IP space, Problem 5.mp4 274.9 MB
10. Min-max problems, best approximations, and least squares/18. Least squares, Problem 11, by projection.mp4 262.4 MB
5. Recurrence relations, dynamical systems, Markov matrices/13. Markov matrices, Problem 8, Restaurant.mp4 252.9 MB
7. Inner product as a generalization of dot product/9. Weighted Euclidean inner product, Problem 1.mp4 252.5 MB
7. Inner product as a generalization of dot product/5. Inner product spaces.mp4 251.5 MB
7. Inner product as a generalization of dot product/19. The evaluation inner products on P2, Problem 5.mp4 240.2 MB
6. Solving systems of linear ODE, and solving higher order ODE/8. System of ODE, Problem 3.mp4 236.1 MB
9. Projections and Gram–Schmidt process in various inner product spaces/5. Orthogonal complements, Problem 2.mp4 229.1 MB
12. Quadratic forms and their classification/14. Classification of curves, Problem 7.mp4 225.8 MB
12. Quadratic forms and their classification/12. Classification of curves, Problem 5.mp4 225.0 MB
9. Projections and Gram–Schmidt process in various inner product spaces/14. Easy computations of IP in ON bases, Problem 8.mp4 218.7 MB
12. Quadratic forms and their classification/18. Quadratic surfaces, Problem 9.mp4 214.8 MB
5. Recurrence relations, dynamical systems, Markov matrices/16. Dynamical systems, Problem 11.mp4 212.6 MB
13. Constrained optimization/1. The theory for this section.mp4 208.6 MB
10. Min-max problems, best approximations, and least squares/3. Min-max, Problem 2.mp4 207.7 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/21. Generalized Theorem of Pythagoras, Problem 8.mp4 207.3 MB
7. Inner product as a generalization of dot product/11. Positive definite matrices.mp4 204.1 MB
11. Diagonalization of symmetric matrices/19. Three tests for definiteness of symmetric matrices, Problem 10.mp4 203.8 MB
7. Inner product as a generalization of dot product/17. Gram matrix for an inner product in the space Pn of polynomials.mp4 197.8 MB
9. Projections and Gram–Schmidt process in various inner product spaces/12. Gram-Schmidt in IP spaces, Problem 6 Legendre polynomials.mp4 193.6 MB
2. Geometrical operators in the plane and in the 3-space/3. Problem 1 Line symmetry in the plane.mp4 193.1 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/8. SVD, Problem 2.mp4 188.2 MB
2. Geometrical operators in the plane and in the 3-space/4. Problem 2 Projection in the plane.mp4 187.2 MB
1. Introduction/1. Introduction.mp4 185.3 MB
6. Solving systems of linear ODE, and solving higher order ODE/9. How to deal with higher order linear ODE.mp4 182.4 MB
5. Recurrence relations, dynamical systems, Markov matrices/6. Systems of difference equations, Problem 3.mp4 178.8 MB
10. Min-max problems, best approximations, and least squares/10. Shortest distance from a subspace.mp4 178.1 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/1. Norm in inner product spaces.mp4 173.4 MB
7. Inner product as a generalization of dot product/22. Inner product in the space of matrices, Problem 6.mp4 170.4 MB
12. Quadratic forms and their classification/16. Some nice visuals on quadratic surfaces.mp4 164.6 MB
10. Min-max problems, best approximations, and least squares/4. Min-max, Problem 3.mp4 164.0 MB
5. Recurrence relations, dynamical systems, Markov matrices/14. Markov matrices, Problem 9, Migration.mp4 163.4 MB
4. Intermezzo isomorphic vector spaces/10. Vector spaces, fields, rings; ring homomorphisms and isomorphisms.mp4 156.3 MB
4. Intermezzo isomorphic vector spaces/8. Isomorphic spaces Problem 2.mp4 156.2 MB
10. Min-max problems, best approximations, and least squares/20. Least squares, fitting a quadratic curve to data, Problem 13.mp4 152.8 MB
5. Recurrence relations, dynamical systems, Markov matrices/2. Two famous examples of recurrence.mp4 151.5 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/4. New facts about AT A eigenvalues and eigenvectors Singular values of A.mp4 148.2 MB
7. Inner product as a generalization of dot product/18. Two inner products on the space of polynomials Pn.mp4 143.3 MB
7. Inner product as a generalization of dot product/16. Inner product in the space of continuous functions.mp4 143.1 MB
11. Diagonalization of symmetric matrices/11. Spectral decomposition for symmetric matrices, Problem 3.mp4 142.2 MB
9. Projections and Gram–Schmidt process in various inner product spaces/6. Orthogonal sets are linearly independent, Problem 3.mp4 139.5 MB
12. Quadratic forms and their classification/2. Completing the square is not unique.mp4 139.0 MB
9. Projections and Gram–Schmidt process in various inner product spaces/8. Projections and orthogonal decomposition in IP spaces.mp4 134.6 MB
2. Geometrical operators in the plane and in the 3-space/8. Another formulation of eigendecomposition Spectral decomposition.mp4 134.0 MB
2. Geometrical operators in the plane and in the 3-space/11. Spectral decomposition, Problem 7.mp4 133.0 MB
12. Quadratic forms and their classification/20. Law of inertia for quadratic forms; Signature of a form, Problem 11.mp4 131.9 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/4. Norm in the space of functions, Problem 2.mp4 129.9 MB
6. Solving systems of linear ODE, and solving higher order ODE/3. Systems of first order linear ODE with constant coefficients.mp4 129.7 MB
4. Intermezzo isomorphic vector spaces/1. You wouldn’t see the difference.mp4 129.7 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/10. Least squares, SVD, and pseudoinverse (Moore-Penrose inverse).mp4 128.3 MB
7. Inner product as a generalization of dot product/6. Euclidean n-space.mp4 126.7 MB
10. Min-max problems, best approximations, and least squares/7. Another look at orthogonal projections as matrix transformations.mp4 126.7 MB
6. Solving systems of linear ODE, and solving higher order ODE/6. System of ODE, Problem 1.mp4 123.6 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/22. Generalized Theorem of Pythagoras, Problem 9.mp4 122.7 MB
12. Quadratic forms and their classification/9. Principal axes; The shortest distance from the origin, Problem 3.mp4 121.9 MB
2. Geometrical operators in the plane and in the 3-space/1. Eigendecomposition, recap.mp4 120.1 MB
11. Diagonalization of symmetric matrices/13. Orthogonal diagonalization, Problem 5.mp4 115.8 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/3. Frobenius norm of matrices, Problem 1.mp4 112.2 MB
10. Min-max problems, best approximations, and least squares/16. Four fundamental matrix spaces and the normal equation.mp4 111.6 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/6. Frobenius distance between matrices, Problem 3.mp4 110.3 MB
9. Projections and Gram–Schmidt process in various inner product spaces/3. Why does normalizing work in the same way in all IP spaces.mp4 109.6 MB
2. Geometrical operators in the plane and in the 3-space/9. Powers of matrices Two methods.mp4 109.5 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/17. Orthogonality in inner product spaces, Problem 7.mp4 104.0 MB
12. Quadratic forms and their classification/8. Quadratic curves by distances; shortest distance from the origin.mp4 102.3 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/20. Generalized Theorem of Pythagoras.mp4 102.0 MB
7. Inner product as a generalization of dot product/23. Frobenius inner product; Hadamard product of matrices.mp4 101.9 MB
12. Quadratic forms and their classification/15. Generally about quadratic surfaces.mp4 101.9 MB
11. Diagonalization of symmetric matrices/15. Orthogonal diagonalization, Problem 7.mp4 100.6 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/5. Distance in inner product spaces.mp4 96.0 MB
11. Diagonalization of symmetric matrices/8. The Spectral Theorem Each symmetric matrix is orthogonally diagonalizable.mp4 95.7 MB
11. Diagonalization of symmetric matrices/3. Eigenvectors corresponding to distinct eigenvalues for a symmetric matrix.mp4 94.8 MB
5. Recurrence relations, dynamical systems, Markov matrices/3. Linear discrete dynamical systems.mp4 84.2 MB
4. Intermezzo isomorphic vector spaces/6. Why you don’t see the difference.mp4 83.9 MB
11. Diagonalization of symmetric matrices/16. Spectral decomposition, Problem 8.mp4 83.3 MB
2. Geometrical operators in the plane and in the 3-space/10. Spectral decomposition, Problem 6.mp4 81.4 MB
6. Solving systems of linear ODE, and solving higher order ODE/4. A very simple example.mp4 78.0 MB
4. Intermezzo isomorphic vector spaces/2. Different spaces with the same structure.mp4 77.1 MB
6. Solving systems of linear ODE, and solving higher order ODE/1. What is an ODE and what kinds of ODE we are going to deal with.mp4 74.4 MB
10. Min-max problems, best approximations, and least squares/12. Shortest distance, Problem 9.mp4 73.9 MB
10. Min-max problems, best approximations, and least squares/1. In this section.mp4 70.6 MB
5. Recurrence relations, dynamical systems, Markov matrices/1. Continuous versus discrete.mp4 70.1 MB
2. Geometrical operators in the plane and in the 3-space/2. Eigendecomposition and operators.mp4 69.9 MB
12. Quadratic forms and their classification/21. Four methods of determining definiteness; Problem 12.mp4 69.7 MB
15. Wrap-up Linear Algebra and Geometry/2. So, what’s next.mp4 69.6 MB
12. Quadratic forms and their classification/7. Quadratic curves as conic sections.mp4 68.0 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/2. Why do we need SVD.mp4 67.6 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/3. We know really a lot about AT A for any rectangular matrix A.mp4 65.2 MB
5. Recurrence relations, dynamical systems, Markov matrices/10. Markov matrices.mp4 64.3 MB
12. Quadratic forms and their classification/3. What kind of questions we want to answer.mp4 63.7 MB
12. Quadratic forms and their classification/10. Classification of quadratic forms in two variables.mp4 61.9 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/12. SVD and Fundamental Theorem of Linear Algebra.mp4 61.6 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/18. What is triangle inequality.mp4 61.3 MB
12. Quadratic forms and their classification/4. 163 Quadratic forms in two variables, Problem 1..mp4 60.1 MB
11. Diagonalization of symmetric matrices/4. Complex numbers a brief repetition.mp4 59.9 MB
6. Solving systems of linear ODE, and solving higher order ODE/2. Solutions to first order linear ODE with constant coefficients.mp4 59.5 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/16. Orthogonality in inner product spaces depends on inner product.mp4 58.6 MB
11. Diagonalization of symmetric matrices/6. Orthogonal diagonalization.mp4 58.5 MB
11. Diagonalization of symmetric matrices/20. Symmetric square roots of symmetric positive definite matrices; singular values.mp4 58.1 MB
7. Inner product as a generalization of dot product/21. Inner product in the space of square matrices.mp4 57.8 MB
6. Solving systems of linear ODE, and solving higher order ODE/7. System of ODE, Problem 2.mp4 57.3 MB
7. Inner product as a generalization of dot product/15. Gram matrix, Problem 4.mp4 55.2 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/13. More weird geometry Angles in inner product spaces, Problem 5.mp4 52.9 MB
11. Diagonalization of symmetric matrices/18. The wonderful strength of an orthogonally diagonalized matrix.mp4 52.0 MB
9. Projections and Gram–Schmidt process in various inner product spaces/11. Gram-Schmidt in IP spaces.mp4 51.9 MB
12. Quadratic forms and their classification/5. Quadratic forms in two variables, Problem 2.mp4 51.8 MB
7. Inner product as a generalization of dot product/2. Dot product in Part 1.mp4 51.7 MB
10. Min-max problems, best approximations, and least squares/8. Orthogonal projections, Problem 6.mp4 50.7 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/2. Weird geometry in the Euclidean space with weighted inner product.mp4 47.5 MB
7. Inner product as a generalization of dot product/3. Dot product and orthogonality in Part 2.mp4 47.3 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/1. All our roads led us to SVD.mp4 47.0 MB
9. Projections and Gram–Schmidt process in various inner product spaces/1. Different but still awesome!.mp4 45.9 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/8. First step to defining abstract angles.mp4 45.3 MB
11. Diagonalization of symmetric matrices/10. Orthogonal diagonalization, Problem 2.mp4 44.5 MB
10. Min-max problems, best approximations, and least squares/13. Shortest distance, Problem 10.mp4 44.1 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/12. Angles in inner product spaces.mp4 43.4 MB
12. Quadratic forms and their classification/6. Quadratic curves, generally.mp4 43.3 MB
7. Inner product as a generalization of dot product/4. From R^2 to inner product spaces.mp4 42.7 MB
13. Constrained optimization/3. Constrained optimization, Problem 2.mp4 42.4 MB
10. Min-max problems, best approximations, and least squares/15. Least squares solution and residual vector.mp4 42.0 MB
13. Constrained optimization/2. Constrained optimization, Problem 1.mp4 41.5 MB
11. Diagonalization of symmetric matrices/2. Some properties of symmetric matrices.mp4 40.2 MB
10. Min-max problems, best approximations, and least squares/14. Solvability of systems of equations in terms of the column space.mp4 39.0 MB
7. Inner product as a generalization of dot product/20. Inner product in the space of m × n matrices.mp4 38.6 MB
4. Intermezzo isomorphic vector spaces/5. A necessary and sufficient condition for isomorphic vector spaces.mp4 38.0 MB
1. Introduction/1.2 Slides Introduction to the course.pdf 37.6 MB
7. Inner product as a generalization of dot product/7. A very important remark about notation.mp4 36.5 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/7. Distance in the space of functions, Problem 4.mp4 35.6 MB
11. Diagonalization of symmetric matrices/9. Orthogonal diagonalization how to do it.mp4 34.9 MB
9. Projections and Gram–Schmidt process in various inner product spaces/7. Coordinates in orthogonal bases in IP spaces.mp4 34.0 MB
4. Intermezzo isomorphic vector spaces/7. Isomorphic spaces Problem 1.mp4 33.8 MB
10. Min-max problems, best approximations, and least squares/11. Shortest distance, Problem 8.mp4 33.7 MB
7. Inner product as a generalization of dot product/8. Inner and outer products.mp4 32.5 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/14. Angles in inner product spaces, Problem 6.mp4 32.4 MB
5. Recurrence relations, dynamical systems, Markov matrices/11. Each Markov matrix has eigenvalue 1.mp4 31.5 MB
4. Intermezzo isomorphic vector spaces/3. More examples of isomorphic vector spaces.mp4 31.0 MB
7. Inner product as a generalization of dot product/1. Between concrete and abstract.mp4 28.9 MB
10. Min-max problems, best approximations, and least squares/9. Orthogonal projections, Problem 7.mp4 28.7 MB
11. Diagonalization of symmetric matrices/7. If a matrix is orthogonally diagonalizable, it is symmetric.mp4 28.5 MB
5. Recurrence relations, dynamical systems, Markov matrices/17. Where to read more on this topic.mp4 27.4 MB
9. Projections and Gram–Schmidt process in various inner product spaces/2. ON bases in IP spaces.mp4 27.3 MB
13. Constrained optimization/4. Constrained optimization, Problem 3.mp4 25.9 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/15. Orthogonality in inner product spaces.mp4 25.9 MB
15. Wrap-up Linear Algebra and Geometry/1. Linear Algebra and Geometry, Wrap-up.mp4 25.6 MB
7. Inner product as a generalization of dot product/10. Remember transposed matrices.mp4 22.5 MB
15. Wrap-up Linear Algebra and Geometry/3. Final words.mp4 22.3 MB
13. Constrained optimization/5. Constrained optimization, Problem 4.mp4 20.3 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/11. Cauchy-Schwarz inequality in the space of continuous functions.mp4 18.8 MB
6. Solving systems of linear ODE, and solving higher order ODE/10.4 Slides Another way of looking at the same problem.pdf 12.8 MB
4. Intermezzo isomorphic vector spaces/1.1 Slides You would not see the difference.pdf 9.1 MB
3. More problem solving; spaces different from R^n/1.1 Notes Eigendecomposition Problem 1.pdf 8.7 MB
7. Inner product as a generalization of dot product/14.1 Notes Gram matrix.pdf 8.3 MB
11. Diagonalization of symmetric matrices/3.1 Slides_Eigenvectors corresponding to distinct eigenvalues for a symmetric matrix are orthogonal.pdf 8.0 MB
11. Diagonalization of symmetric matrices/1.2 Slides_The link between symmetric matrices and quadratic forms Problem 1.pdf 7.8 MB
12. Quadratic forms and their classification/20.1 Slides_Law of inertia for quadratic forms; Signature of a form Problem 11.pdf 7.8 MB
10. Min-max problems, best approximations, and least squares/13.1 Slides_Shortest distance Problem 10.pdf 7.3 MB
7. Inner product as a generalization of dot product/21.1 Slides Inner products in the space of square matrices.pdf 7.2 MB
3. More problem solving; spaces different from R^n/5.1 Notes In the space of polynomials Problem 5.pdf 6.7 MB
4. Intermezzo isomorphic vector spaces/12.1 Notes Vector spaces Fields Rings Problem 5.pdf 6.1 MB
10. Min-max problems, best approximations, and least squares/7.1 Slides_Another look at orthogonal projections as matrix transformations.pdf 6.1 MB
3. More problem solving; spaces different from R^n/4.1 Notes Powers and roots Problem 4.pdf 6.1 MB
2. Geometrical operators in the plane and in the 3-space/8.1 Slides Another formulation of eigendecomposition Spectral.pdf 6.0 MB
11. Diagonalization of symmetric matrices/16.1 Slides_Spectral decomposition Problem 8.pdf 5.9 MB
6. Solving systems of linear ODE, and solving higher order ODE/3.1 Slides Systems of first order linear ODE with constant coefficients.pdf 5.9 MB
11. Diagonalization of symmetric matrices/14.1 Notes_Orthogonal diagonalization Problem 6.pdf 5.6 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/14.1 Slides_Angles in inner product spaces Problem 6.pdf 5.5 MB
3. More problem solving; spaces different from R^n/6.2 Slides In the space of polynomials Problem 6.pdf 5.5 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/9.1 Notes_Cauchy--Schwarz inequality Proof 1.pdf 5.3 MB
7. Inner product as a generalization of dot product/13.1 Notes Matrix inner product on Rn.pdf 5.3 MB
12. Quadratic forms and their classification/19.1 Notes_Quadratic surfaces Problem 10.pdf 5.2 MB
3. More problem solving; spaces different from R^n/7.1 Notes In the space of matrices Problem 7.pdf 5.2 MB
6. Solving systems of linear ODE, and solving higher order ODE/5.2 Slides The method.pdf 5.2 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/5.1 Notes_ON bases containing only eigenvectors of certain matrix products.pdf 5.2 MB
3. More problem solving; spaces different from R^n/2.1 Notes Eigendecomposition Problem 2.pdf 5.1 MB
2. Geometrical operators in the plane and in the 3-space/9.1 Slides Powers of matrices Two methods.pdf 5.1 MB
9. Projections and Gram–Schmidt process in various inner product spaces/4.2 Notes_Orthonormal sets of continuous functions Problem 1.pdf 5.1 MB
12. Quadratic forms and their classification/1.1 Notes_The correspondence between quadratic forms and symmetric matrices is 1to1.pdf 5.1 MB
12. Quadratic forms and their classification/14.2 Slides_Classification of curves Problem 7.pdf 5.0 MB
12. Quadratic forms and their classification/10.1 Slides_Classification of quadratic forms in two variables.pdf 5.0 MB
2. Geometrical operators in the plane and in the 3-space/7.1 Notes Problem 5 Projection in the 3 space.pdf 5.0 MB
2. Geometrical operators in the plane and in the 3-space/11.1 Slides Spectral decomposition Problem 7.pdf 4.9 MB
6. Solving systems of linear ODE, and solving higher order ODE/8.1 Notes System of ODE Problem 3.pdf 4.8 MB
3. More problem solving; spaces different from R^n/3.1 Notes Powers and roots Problem 3.pdf 4.8 MB
5. Recurrence relations, dynamical systems, Markov matrices/4.1 Notes Systems of difference equations Problem 1.pdf 4.8 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/6.2 Slides_Singular value decomposition with proof and geometric interpretation.pdf 4.8 MB
2. Geometrical operators in the plane and in the 3-space/12.2 Slides Spectral decomposition Geometrical illustration.pdf 4.7 MB
11. Diagonalization of symmetric matrices/12.1 Notes_Orthogonal diagonalization Problem 4.pdf 4.7 MB
4. Intermezzo isomorphic vector spaces/7.1 Slides Isomorphic spaces Problem 1.pdf 4.7 MB
5. Recurrence relations, dynamical systems, Markov matrices/13.1 Notes Markov matrices Problem 8 Restaurant.pdf 4.7 MB
11. Diagonalization of symmetric matrices/5.1 Notes_Eigenvalues for a (real) symmetric matrix are real.pdf 4.6 MB
11. Diagonalization of symmetric matrices/19.1 Notes_Three tests for definiteness of symmetric matrices Problem 10.pdf 4.4 MB
2. Geometrical operators in the plane and in the 3-space/10.1 Slides Spectral decomposition Problem 6.pdf 4.3 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/9.1 Notes_More new facts about ATA Six equivalent statements.pdf 4.1 MB
11. Diagonalization of symmetric matrices/11.1 Slides_Spectral decomposition for symmetric matrices Problem 3.pdf 4.1 MB
4. Intermezzo isomorphic vector spaces/4.1 Notes A necessary condition for isomorphic vector spaces.pdf 4.1 MB
2. Geometrical operators in the plane and in the 3-space/1.1 Slides Eigendecomposition recap.pdf 4.1 MB
11. Diagonalization of symmetric matrices/6.1 Slides_Orthogonal diagonalization.pdf 3.9 MB
12. Quadratic forms and their classification/17.1 Notes_Quadratic surfaces Shortest distance Problem 8.pdf 3.9 MB
12. Quadratic forms and their classification/21.2 Slides_Four methods of determining definiteness Problem 12.pdf 3.9 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/7.1 Notes_SVD, reduced singular value decomposition Problem 1.pdf 3.9 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/6.1 Notes_Singular value decomposition with proof and geometric interpretation.pdf 3.9 MB
4. Intermezzo isomorphic vector spaces/11.1 Notes Vector spaces Fields Rings Problem 4.pdf 3.8 MB
7. Inner product as a generalization of dot product/5.1 Notes Inner product spaces.pdf 3.8 MB
13. Constrained optimization/1.1 Slides_The theory for this section.pdf 3.8 MB
10. Min-max problems, best approximations, and least squares/5.1 Notes_Min max Problem 4.pdf 3.8 MB
4. Intermezzo isomorphic vector spaces/9.1 Notes Isomorphic spaces Problem 3.pdf 3.8 MB
10. Min-max problems, best approximations, and least squares/17.1 Notes_Least squares Problem 11 by normal equation.pdf 3.7 MB
9. Projections and Gram–Schmidt process in various inner product spaces/13.1 Notes_Gram Schmidt in IP spaces Problem 7.pdf 3.7 MB
7. Inner product as a generalization of dot product/12.1 Notes Quadratic forms and how to read them.pdf 3.6 MB
9. Projections and Gram–Schmidt process in various inner product spaces/10.1 Notes_Projections and orthogonal decomposition in IP spaces Problem 5.pdf 3.6 MB
10. Min-max problems, best approximations, and least squares/2.1 Notes_Min max Problem 1.pdf 3.5 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/4.3 Slides_New facts about ATA eigenvalues and eigenvectors Singular values of A.pdf 3.5 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/23.1 Notes_Generalized Theorem of Pythagoras Problem 10.pdf 3.5 MB
10. Min-max problems, best approximations, and least squares/18.1 Notes_Least squares Problem 11 by projection.pdf 3.5 MB
10. Min-max problems, best approximations, and least squares/3.1 Notes_Min max Problem 2.pdf 3.5 MB
5. Recurrence relations, dynamical systems, Markov matrices/7.1 Notes Higher order difference equations Problem 4.pdf 3.4 MB
12. Quadratic forms and their classification/13.2 Slides_Different roles of symmetric matrices Problem 6.pdf 3.4 MB
10. Min-max problems, best approximations, and least squares/20.1 Notes_Least squares Fitting a quadratic curve to data Problem 13.pdf 3.4 MB
5. Recurrence relations, dynamical systems, Markov matrices/16.1 Notes Dynamical systems Problem 11.pdf 3.4 MB
7. Inner product as a generalization of dot product/22.1 Notes Inner product in the space of matrices Problem 6.pdf 3.4 MB
10. Min-max problems, best approximations, and least squares/12.1 Slides_Shortest distance Problem 9.pdf 3.4 MB
7. Inner product as a generalization of dot product/17.1 Slides Gram matrix for an inner product in the space P_n of polynomials.pdf 3.1 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/19.1 Notes_Triangle inequality in inner product spaces.pdf 2.9 MB
12. Quadratic forms and their classification/9.1 Slides_Principal axes Shortest distance Problem 3.pdf 2.9 MB
7. Inner product as a generalization of dot product/9.1 Notes Weighted Euclidean inner product Problem 1.pdf 2.9 MB
9. Projections and Gram–Schmidt process in various inner product spaces/9.1 Notes_Projections and orthogonal decomposition in IP spaces Problem 4.pdf 2.9 MB
13. Constrained optimization/3.1 Slides_Constrained optimization Problem 2.pdf 2.8 MB
10. Min-max problems, best approximations, and least squares/1.1 Slides_In this section.pdf 2.8 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/10.1 Notes_Cauchy--Schwarz inequality Proof 2.pdf 2.8 MB
11. Diagonalization of symmetric matrices/17.2 Notes_Positive and negative definite matrices semidefinite and indefinite matrices Problem 9.pdf 2.7 MB
13. Constrained optimization/2.1 Slides_Constrained optimization Problem 1.pdf 2.7 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/11.1 Notes_Pseudoinverse Problem 3.pdf 2.7 MB
6. Solving systems of linear ODE, and solving higher order ODE/10.3 Notes Another way of looking at the same problem.pdf 2.7 MB
5. Recurrence relations, dynamical systems, Markov matrices/5.1 Notes Systems of difference equations Problem 2.pdf 2.7 MB
5. Recurrence relations, dynamical systems, Markov matrices/9.1 Notes Higher order difference equations Problem 6.pdf 2.7 MB
10. Min-max problems, best approximations, and least squares/6.1 Notes_Min max Problem 5.pdf 2.7 MB
6. Solving systems of linear ODE, and solving higher order ODE/4.1 Slides A very simple example.pdf 2.7 MB
6. Solving systems of linear ODE, and solving higher order ODE/5.1 Notes The method.pdf 2.6 MB
12. Quadratic forms and their classification/5.1 Slides_Quadratic forms in two variables Problem 2.pdf 2.6 MB
7. Inner product as a generalization of dot product/16.1 Notes Inner product in the space of continuous functions.pdf 2.6 MB
10. Min-max problems, best approximations, and least squares/2.2 Slides_Min max Problem 1.pdf 2.5 MB
12. Quadratic forms and their classification/18.1 Notes_Quadratic surfaces Problem 9.pdf 2.5 MB
5. Recurrence relations, dynamical systems, Markov matrices/15.1 Notes Markov matrices Problem 10 Election.pdf 2.5 MB
12. Quadratic forms and their classification/13.1 Notes_Different roles of symmetric matrices Problem 6.pdf 2.5 MB
2. Geometrical operators in the plane and in the 3-space/12.1 Notes Spectral decomposition Geometrical illustration.pdf 2.5 MB
10. Min-max problems, best approximations, and least squares/19.1 Notes_Least squares Fitting a line Problem 12.pdf 2.5 MB
7. Inner product as a generalization of dot product/19.1 Notes The evaluation inner products on P2 Problem 5.pdf 2.5 MB
5. Recurrence relations, dynamical systems, Markov matrices/12.1 Notes Steady state vector Equilibrium vector Problem 7.pdf 2.5 MB
5. Recurrence relations, dynamical systems, Markov matrices/8.1 Notes Higher order difference equations Problem 5.pdf 2.4 MB
11. Diagonalization of symmetric matrices/10.1 Slides_Orthogonal diagonalization Problem 2.pdf 2.4 MB
12. Quadratic forms and their classification/11.1 Notes_Classification of curves Problem 4.pdf 2.4 MB
11. Diagonalization of symmetric matrices/20.1 Slides_Symmetric square roots of symmetric positive definite matrices Singular values Problem 11.pdf 2.4 MB
6. Solving systems of linear ODE, and solving higher order ODE/6.1 Slides System of ODE Problem 1.pdf 2.4 MB
4. Intermezzo isomorphic vector spaces/8.1 Notes Isomorphic spaces Problem 2.pdf 2.4 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/16.1 Slides_Orthogonality in inner product spaces depends on inner product.pdf 2.4 MB
11. Diagonalization of symmetric matrices/1.1 Notes_The link between symmetric matrices and quadratic forms Problem 1.pdf 2.4 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/8.1 Notes_SVD Problem 2.pdf 2.3 MB
9. Projections and Gram–Schmidt process in various inner product spaces/12.1 Notes_Gram Schmidt in IP spaces Problem 6 Legendre polynomials.pdf 2.3 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/5.1 Notes_Distance in inner product spaces.pdf 2.3 MB
11. Diagonalization of symmetric matrices/5.2 Slides_Eigenvalues for a (real) symmetric matrix are real.pdf 2.2 MB
6. Solving systems of linear ODE, and solving higher order ODE/7.1 Slides System of ODE Problem 2.pdf 2.2 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/22.1 Notes_Generalized Theorem of Pythagoras Problem 9.pdf 2.2 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/10.1 Slides_Least squares, SVD, and pseudoinverse Moore Penrose inverse.pdf 2.2 MB
7. Inner product as a generalization of dot product/2.1 Slides Dot product in Part 1.pdf 2.2 MB
11. Diagonalization of symmetric matrices/19.2 Slides_Three tests for definiteness of symmetric matrices Problem 10.pdf 2.2 MB
7. Inner product as a generalization of dot product/15.1 Slides Gram matrix Problem 4.pdf 2.1 MB
9. Projections and Gram–Schmidt process in various inner product spaces/1.1 Slides_Different but still awesome.pdf 2.1 MB
12. Quadratic forms and their classification/15.1 Slides_Generally about quadratic surfaces.pdf 2.1 MB
2. Geometrical operators in the plane and in the 3-space/6.1 Notes Problem 4 Projection in the 3 space.pdf 2.1 MB
13. Constrained optimization/4.1 Slides_Constrained optimization Problem 3.pdf 2.0 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/22.2 Slides_Generalized Theorem of Pythagoras Problem 9.pdf 2.0 MB
6. Solving systems of linear ODE, and solving higher order ODE/10.1 Article-Solved-Problems-Eigenvalues-ODE.pdf 1.9 MB
11. Diagonalization of symmetric matrices/18.1 Slides_The wonderful strength of an orthogonally diagonalized matrix.pdf 1.9 MB
7. Inner product as a generalization of dot product/3.1 Slides Dot product and orthogonality in Part 2.pdf 1.9 MB
6. Solving systems of linear ODE, and solving higher order ODE/9.3 Slides How to deal with higher order linear ODE.pdf 1.9 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/19.2 Slides_Triangle inequality in inner product spaces.pdf 1.8 MB
9. Projections and Gram–Schmidt process in various inner product spaces/12.2 Slides_Gram Schmidt in IP spaces Problem 6 Legendre polynomials.pdf 1.8 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/9.2 Slides_More new facts about ATA Six equivalent statements.pdf 1.8 MB
11. Diagonalization of symmetric matrices/17.3 Slides_Positive and negative definite matrices semidefinite and indefinite matrices Problem 9.pdf 1.7 MB
5. Recurrence relations, dynamical systems, Markov matrices/4.2 Slides Systems of difference equations Problem 1.pdf 1.6 MB
7. Inner product as a generalization of dot product/23.1 Slides_Frobenius inner product and Hadamard product of matrices.pdf 1.6 MB
6. Solving systems of linear ODE, and solving higher order ODE/2.1 Slides Solutions to first order linear ODE with constant coefficients.pdf 1.5 MB
10. Min-max problems, best approximations, and least squares/10.1 Notes_Shortest distance from a subspace.pdf 1.5 MB
15. Wrap-up Linear Algebra and Geometry/1.1 Slides_Linear Algebra and Geometry Wrap up.pdf 1.5 MB
7. Inner product as a generalization of dot product/11.1 Notes Positive definite matrices.pdf 1.5 MB
12. Quadratic forms and their classification/8.1 Slides_Quadratic curves by distances Shortest distance from the origin.pdf 1.5 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/8.2 Slides_SVD Problem 2.pdf 1.5 MB
7. Inner product as a generalization of dot product/18.1 Notes Two inner products in the space of polynomials.pdf 1.5 MB
3. More problem solving; spaces different from R^n/6.1 Notes In the space of polynomials Problem 6.pdf 1.5 MB
7. Inner product as a generalization of dot product/6.1 Notes Euclidean n-space.pdf 1.4 MB
7. Inner product as a generalization of dot product/10.1 Slides Remember transposed matrices.pdf 1.4 MB
7. Inner product as a generalization of dot product/13.2 Slides Matrix inner product on Rn.pdf 1.4 MB
12. Quadratic forms and their classification/1.2 Slides_The correspondence between quadratic forms and symmetric matrices is 1to1.pdf 1.4 MB
5. Recurrence relations, dynamical systems, Markov matrices/17.1 Slides Where to read more on this topic.pdf 1.4 MB
5. Recurrence relations, dynamical systems, Markov matrices/2.1 Notes Two famous examples of recurrence.pdf 1.4 MB
10. Min-max problems, best approximations, and least squares/4.1 Notes_Min max Problem 3.pdf 1.4 MB
9. Projections and Gram–Schmidt process in various inner product spaces/8.1 Notes_Projections and orthogonal decomposition in IP spaces.pdf 1.4 MB
5. Recurrence relations, dynamical systems, Markov matrices/14.1 Notes Markov matrices Problem 9 Migration.pdf 1.3 MB
11. Diagonalization of symmetric matrices/15.1 Notes_Orthogonal diagonalization Problem 7.pdf 1.3 MB
2. Geometrical operators in the plane and in the 3-space/5.1 Notes Problem 3 Symmetry in the 3 space.pdf 1.3 MB
7. Inner product as a generalization of dot product/11.2 Slides Positive definite matrices.pdf 1.3 MB
9. Projections and Gram–Schmidt process in various inner product spaces/5.1 Notes_Orthogonal complements Problem 2.pdf 1.3 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/21.1 Notes_Generalized Theorem of Pythagoras Problem 8.pdf 1.3 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/1.1 Notes_Norm in inner product spaces.pdf 1.3 MB
2. Geometrical operators in the plane and in the 3-space/3.2 Slides Problem 1 Line symmetry in the plane.pdf 1.3 MB
12. Quadratic forms and their classification/12.1 Notes_Classification of curves Problem 5.pdf 1.3 MB
9. Projections and Gram–Schmidt process in various inner product spaces/3.1 Notes_Why does normalizing work in the same way in all IP spaces.pdf 1.3 MB
6. Solving systems of linear ODE, and solving higher order ODE/9.2 Notes How to deal with higher order linear ODE.pdf 1.3 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/13.1 Slides_More weird geometry Angles in inner product spaces Problem 5.pdf 1.3 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/4.2 Notes_New facts about ATA eigenvalues and eigenvectors Singular values of A.pdf 1.3 MB
11. Diagonalization of symmetric matrices/13.1 Notes_Orthogonal diagonalization Problem 5.pdf 1.3 MB
9. Projections and Gram–Schmidt process in various inner product spaces/6.1 Notes_Orthogonal sets are linearly independent Problem 3.pdf 1.3 MB
5. Recurrence relations, dynamical systems, Markov matrices/6.1 Notes Systems of difference equations Problem 3.pdf 1.3 MB
7. Inner product as a generalization of dot product/14.2 Slides Gram matrix.pdf 1.2 MB
10. Min-max problems, best approximations, and least squares/16.1 Slides_Four fundamental matrix spaces and the normal equation.pdf 1.2 MB
5. Recurrence relations, dynamical systems, Markov matrices/12.2 Slides Steady state vector Equilibrium vector Problem 7.pdf 1.2 MB
12. Quadratic forms and their classification/2.1 Notes_Completing the square is not unique.pdf 1.2 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/17.1 Notes_Orthogonality in inner product spaces Problem 7.pdf 1.2 MB
2. Geometrical operators in the plane and in the 3-space/4.2 Slides Problem 2 Projection in the plane.pdf 1.2 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/12.1 Slides_SVD and Fundamental Theorem of Linear Algebra.pdf 1.2 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/20.1 Notes_Generalized Theorem of Pythagoras.pdf 1.2 MB
12. Quadratic forms and their classification/14.1 Notes_Classification of curves Problem 7.pdf 1.2 MB
4. Intermezzo isomorphic vector spaces/10.1 Slides Vector spaces Fields Rings Ring isomorphisms.pdf 1.2 MB
6. Solving systems of linear ODE, and solving higher order ODE/1.1 Slides What is an ODE and what kinds of ODE we are going to deal with.pdf 1.2 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/4.1 Notes_Norm in the space of functions Problem 2.pdf 1.2 MB
9. Projections and Gram–Schmidt process in various inner product spaces/14.3 Slides_Easy computations of IP in ON bases Problem 8.pdf 1.2 MB
6. Solving systems of linear ODE, and solving higher order ODE/9.1 Article-Supplement-to-Video-81-in-Part2-Non-homogenous-ODE.pdf 1.2 MB
9. Projections and Gram–Schmidt process in various inner product spaces/14.2 Notes_Easy computations of IP in ON bases Problem 8.pdf 1.2 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/6.1 Notes_Frobenius distance between matrices Problem 3.pdf 1.2 MB
13. Constrained optimization/5.1 Slides_Constrained optimization Problem 4.pdf 1.2 MB
12. Quadratic forms and their classification/21.1 Article-Solved-Problems-Quadratic-Forms.pdf 1.1 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/3.1 Notes_Frobenius norm of matrices Problem 1.pdf 1.1 MB
10. Min-max problems, best approximations, and least squares/11.1 Slides_Shortest distance Problem 8.pdf 1.1 MB
4. Intermezzo isomorphic vector spaces/4.2 Slides A necessary condition for isomorphic vector spaces.pdf 1.0 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/7.1 Slides_Distance in the space of functions Problem 4.pdf 1.0 MB
9. Projections and Gram–Schmidt process in various inner product spaces/8.2 Slides_Projections and orthogonal decomposition in IP spaces.pdf 1.0 MB
3. More problem solving; spaces different from R^n/5.2 Slides In the space of polynomials Problem 5.pdf 1014.0 KB
6. Solving systems of linear ODE, and solving higher order ODE/10.2 Article-Theory-Eigenvalues-ODE.pdf 975.4 KB
10. Min-max problems, best approximations, and least squares/8.1 Slides_Orthogonal projections Problem 6.pdf 974.1 KB
9. Projections and Gram–Schmidt process in various inner product spaces/11.1 Slides_Gram Schmidt in IP spaces.pdf 969.0 KB
9. Projections and Gram–Schmidt process in various inner product spaces/5.2 Slides_Orthogonal complements Problem 2.pdf 962.9 KB
4. Intermezzo isomorphic vector spaces/5.1 Slides A necessary and sufficient condition for isomorphic vector spaces.pdf 950.9 KB
11. Diagonalization of symmetric matrices/7.1 Slides_If a matrix is orthogonally diagonalizable it is symmetric.pdf 903.1 KB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/7.2 Slides_SVD, reduced singular value decomposition Problem 1.pdf 860.2 KB
12. Quadratic forms and their classification/16.1 Slides_Some nice visuals on quadratic surfaces.pdf 849.5 KB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/5.2 Slides_ON bases containing only eigenvectors of certain matrix products.pdf 836.4 KB
4. Intermezzo isomorphic vector spaces/11.2 Slides Vector spaces Fields Rings Problem 4.pdf 817.7 KB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/3.1 Slides_We know really a lot about ATA for any rectangular matrix A.pdf 815.7 KB
12. Quadratic forms and their classification/19.2 Slides_Quadratic surfaces Problem 10.pdf 790.2 KB
3. More problem solving; spaces different from R^n/3.2 Slides Powers and roots Problem 3.pdf 767.8 KB
10. Min-max problems, best approximations, and least squares/9.1 Slides_Orthogonal projections Problem 7.pdf 753.3 KB
8. Norm, distance, angles, and orthogonality in inner product spaces/23.2 Slides_Generalized Theorem of Pythagoras Problem 10.pdf 751.7 KB
12. Quadratic forms and their classification/17.2 Slides_Quadratic surfaces Shortest distance Problem 8.pdf 751.6 KB
7. Inner product as a generalization of dot product/8.1 Slides Inner and outer products.pdf 730.5 KB
7. Inner product as a generalization of dot product/12.2 Slides Quadratic forms and how to read them.pdf 723.3 KB
9. Projections and Gram–Schmidt process in various inner product spaces/13.2 Slides_Gram Schmidt in IP spaces Problem 7.pdf 718.8 KB
4. Intermezzo isomorphic vector spaces/6.1 Slides Why you dont see the difference.pdf 712.2 KB
10. Min-max problems, best approximations, and least squares/3.2 Slides_Min max Problem 2.pdf 701.9 KB
12. Quadratic forms and their classification/18.2 Slides_Quadratic surfaces Problem 9.pdf 698.0 KB
8. Norm, distance, angles, and orthogonality in inner product spaces/18.1 Slides_What is triangle inequality.pdf 689.9 KB
6. Solving systems of linear ODE, and solving higher order ODE/8.2 Slides System of ODE Problem 3.pdf 666.6 KB
8. Norm, distance, angles, and orthogonality in inner product spaces/15.1 Slides_Orthogonality in inner product spaces.pdf 645.3 KB
8. Norm, distance, angles, and orthogonality in inner product spaces/8.1 Slides_First step to defining abstract angles.pdf 639.9 KB
2. Geometrical operators in the plane and in the 3-space/2.1 Slides Eigendecomposition and operators.pdf 638.6 KB
2. Geometrical operators in the plane and in the 3-space/4.1 Notes Problem 2 Projection in the plane.pdf 633.9 KB
2. Geometrical operators in the plane and in the 3-space/3.1 Notes Problem 1 Line symmetry in the plane.pdf 563.2 KB
8. Norm, distance, angles, and orthogonality in inner product spaces/1.2 Slides_Norm in inner product spaces.pdf 561.9 KB
9. Projections and Gram–Schmidt process in various inner product spaces/4.3 Slides_Orthonormal sets of continuous functions Problem 1.pdf 554.5 KB
8. Norm, distance, angles, and orthogonality in inner product spaces/3.2 Slides_Frobenius norm of matrices Problem 1.pdf 546.4 KB
8. Norm, distance, angles, and orthogonality in inner product spaces/2.1 Slides_Weird geometry in the Euclidean space with weighted inner product.pdf 533.5 KB
1. Introduction/1.1 List_of_all_Videos_and_Problems_Linear_Algebra_and_Geometry_3.pdf 528.9 KB
10. Min-max problems, best approximations, and least squares/18.2 Slides_Least squares Problem 11 by projection.pdf 520.2 KB
9. Projections and Gram–Schmidt process in various inner product spaces/6.2 Slides_Orthogonal sets are linearly independent Problem 3.pdf 515.6 KB
4. Intermezzo isomorphic vector spaces/2.1 Slides Different spaces with the same structure.pdf 498.7 KB
7. Inner product as a generalization of dot product/5.2 Slides Inner product spaces.pdf 498.2 KB
10. Min-max problems, best approximations, and least squares/17.2 Slides_Least squares Problem 11 by normal equation.pdf 487.4 KB
7. Inner product as a generalization of dot product/9.2 Slides Weighted Euclidean inner product Problem 1.pdf 468.3 KB
7. Inner product as a generalization of dot product/22.2 Slides Inner product in the space of matrices Problem 6.pdf 458.5 KB
4. Intermezzo isomorphic vector spaces/12.2 Slides Vector spaces Fields Rings Problem 5.pdf 452.9 KB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/2.1 Slides_Why do we need SVD.pdf 446.9 KB
9. Projections and Gram–Schmidt process in various inner product spaces/9.2 Slides_Projections and orthogonal decomposition in IP spaces Problem 4.pdf 443.4 KB
11. Diagonalization of symmetric matrices/8.2 Slides_The Spectral Theorem Each symmetric matrix is orthogonally diagonalizable.pdf 422.2 KB
5. Recurrence relations, dynamical systems, Markov matrices/9.2 Slides Higher order difference equations Problem 6.pdf 417.3 KB
7. Inner product as a generalization of dot product/7.1 Slides A very important remark about notation.pdf 414.6 KB
8. Norm, distance, angles, and orthogonality in inner product spaces/6.2 Slides_Frobenius distance between matrices Problem 3.pdf 395.6 KB
8. Norm, distance, angles, and orthogonality in inner product spaces/4.2 Slides_Norm in the space of functions Problem 2.pdf 392.9 KB
7. Inner product as a generalization of dot product/4.1 Slides From R^2 to inner product spaces.pdf 390.4 KB
4. Intermezzo isomorphic vector spaces/9.2 Slides Isomorphic spaces Problem 3.pdf 387.8 KB
7. Inner product as a generalization of dot product/18.2 Slides Two inner products in the space of polynomials.pdf 387.8 KB
7. Inner product as a generalization of dot product/16.2 Slides Inner product in the space of continuous functions.pdf 385.6 KB
8. Norm, distance, angles, and orthogonality in inner product spaces/9.2 Slides_Cauchy--Schwarz inequality Proof 1.pdf 383.9 KB
5. Recurrence relations, dynamical systems, Markov matrices/14.2 Slides Markov matrices Problem 9 Migration.pdf 374.2 KB
9. Projections and Gram–Schmidt process in various inner product spaces/10.2 Slides_Projections and orthogonal decomposition in IP spaces Problem 5.pdf 370.6 KB
9. Projections and Gram–Schmidt process in various inner product spaces/14.1 Article-Solved-Problems-Projections-In-Matrix-Spaces.pdf 368.3 KB
10. Min-max problems, best approximations, and least squares/19.2 Slides_Least squares Fitting a line Problem 12.pdf 366.2 KB
12. Quadratic forms and their classification/4.1 Slides_Quadratic forms in two variables Problem 1.pdf 361.7 KB
5. Recurrence relations, dynamical systems, Markov matrices/2.2 Slides Two famous examples of recurrence.pdf 360.9 KB
2. Geometrical operators in the plane and in the 3-space/6.2 Slides Problem 4 Projection in the 3 space.pdf 353.6 KB
7. Inner product as a generalization of dot product/20.1 Slides Inner products in the space of m by n matrices.pdf 350.5 KB
7. Inner product as a generalization of dot product/19.2 Slides The evaluation inner products on P2 Problem 5.pdf 348.3 KB
9. Projections and Gram–Schmidt process in various inner product spaces/2.1 Slides_ON bases in IP spaces.pdf 345.7 KB
9. Projections and Gram–Schmidt process in various inner product spaces/7.1 Slides_Coordinates in orthogonal bases in IP spaces.pdf 345.5 KB
11. Diagonalization of symmetric matrices/4.1 Slides_Complex numbers A brief repetition.pdf 339.6 KB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/11.2 Slides_Pseudoinverse Problem 3.pdf 338.5 KB
11. Diagonalization of symmetric matrices/12.2 Slides_Orthogonal diagonalization Problem 4.pdf 333.6 KB
10. Min-max problems, best approximations, and least squares/5.2 Slides_Min max Problem 4.pdf 332.8 KB
12. Quadratic forms and their classification/3.1 Slides_What kind of questions we want to answer.pdf 328.1 KB
12. Quadratic forms and their classification/7.1 Slides_Quadratic curves as conic sections.pdf 327.6 KB
2. Geometrical operators in the plane and in the 3-space/5.2 Slides Problem 3 Symmetry in the 3 space.pdf 326.9 KB
12. Quadratic forms and their classification/2.2 Slides_Completing the square is not unique.pdf 326.7 KB
10. Min-max problems, best approximations, and least squares/6.2 Slides_Min max Problem 5.pdf 313.3 KB
10. Min-max problems, best approximations, and least squares/14.1 Slides_Solvability of systems of equations in terms of the column space.pdf 310.5 KB
12. Quadratic forms and their classification/6.1 Slides_Quadratic curves Generally.pdf 310.5 KB
8. Norm, distance, angles, and orthogonality in inner product spaces/5.2 Slides_Distance in inner product spaces.pdf 310.3 KB
5. Recurrence relations, dynamical systems, Markov matrices/13.2 Slides Markov matrices Problem 8 Restaurant.pdf 310.3 KB
10. Min-max problems, best approximations, and least squares/4.2 Slides_Min max Problem 3.pdf 307.1 KB
5. Recurrence relations, dynamical systems, Markov matrices/16.2 Slides Dynamical systems Problem 11.pdf 306.2 KB
2. Geometrical operators in the plane and in the 3-space/7.2 Slides Problem 5 Projection in the 3 space.pdf 306.1 KB
8. Norm, distance, angles, and orthogonality in inner product spaces/12.1 Slides_Angles in inner product spaces.pdf 303.7 KB
5. Recurrence relations, dynamical systems, Markov matrices/10.1 Slides Markov matrices.pdf 303.5 KB
12. Quadratic forms and their classification/12.2 Slides_Classification of curves Problem 5.pdf 300.1 KB
12. Quadratic forms and their classification/11.2 Slides_Classification of curves Problem 4.pdf 296.1 KB
8. Norm, distance, angles, and orthogonality in inner product spaces/17.2 Slides_Orthogonality in inner product spaces Problem 7.pdf 292.5 KB
3. More problem solving; spaces different from R^n/1.2 Slides Eigendecomposition Problem 1.pdf 284.9 KB
7. Inner product as a generalization of dot product/6.2 Slides Euclidean n-space.pdf 279.0 KB
10. Min-max problems, best approximations, and least squares/20.2 Slides_Least squares Fitting a quadratic curve to data Problem 13.pdf 273.0 KB
8. Norm, distance, angles, and orthogonality in inner product spaces/20.2 Slides_Generalized Theorem of Pythagoras.pdf 270.9 KB
4. Intermezzo isomorphic vector spaces/8.2 Slides Isomorphic spaces Problem 2.pdf 259.1 KB
8. Norm, distance, angles, and orthogonality in inner product spaces/21.2 Slides_Generalized Theorem of Pythagoras Problem 8.pdf 245.9 KB
5. Recurrence relations, dynamical systems, Markov matrices/7.2 Slides Higher order difference equations Problem 4.pdf 241.8 KB
4. Intermezzo isomorphic vector spaces/3.1 Slides More examples of isomorphic vector spaces.pdf 240.5 KB
11. Diagonalization of symmetric matrices/14.2 Slides_Orthogonal diagonalization Problem 6.pdf 239.3 KB
11. Diagonalization of symmetric matrices/15.2 Slides_Orthogonal diagonalization Problem 7.pdf 237.6 KB
5. Recurrence relations, dynamical systems, Markov matrices/3.1 Slides Linear discrete dynamical systems.pdf 231.0 KB
3. More problem solving; spaces different from R^n/4.2 Slides Powers and roots Problem 4.pdf 228.5 KB
5. Recurrence relations, dynamical systems, Markov matrices/5.2 Slides Systems of difference equations Problem 2.pdf 221.1 KB
8. Norm, distance, angles, and orthogonality in inner product spaces/10.2 Slides_Cauchy--Schwarz inequality Proof 2.pdf 214.8 KB
11. Diagonalization of symmetric matrices/13.2 Slides_Orthogonal diagonalization Problem 5.pdf 210.3 KB
3. More problem solving; spaces different from R^n/2.2 Slides Eigendecomposition Problem 2.pdf 205.4 KB
3. More problem solving; spaces different from R^n/7.2 Slides In the space of matrices Problem 7.pdf 202.7 KB
11. Diagonalization of symmetric matrices/9.1 Slides_Orthogonal diagonalization How to do it.pdf 200.9 KB
5. Recurrence relations, dynamical systems, Markov matrices/1.1 Slides Continuous versus discrete.pdf 193.0 KB
5. Recurrence relations, dynamical systems, Markov matrices/6.2 Slides Systems of difference equations Problem 3.pdf 191.3 KB
5. Recurrence relations, dynamical systems, Markov matrices/8.2 Slides Higher order difference equations Problem 5.pdf 184.5 KB
10. Min-max problems, best approximations, and least squares/15.1 Slides_Least squares solution and residual vector.pdf 167.6 KB
10. Min-max problems, best approximations, and least squares/10.2 Slides_Shortest distance from a subspace.pdf 156.8 KB
5. Recurrence relations, dynamical systems, Markov matrices/15.2 Slides Markov matrices Problem 10 Election.pdf 156.8 KB
11. Diagonalization of symmetric matrices/8.1 Article-Spectral-Theorem-Proof-of-Lemma-2.pdf 149.1 KB
5. Recurrence relations, dynamical systems, Markov matrices/11.1 Slides Each Markov matrix has eigenvalue one.pdf 144.6 KB
9. Projections and Gram–Schmidt process in various inner product spaces/4.1 Article-Riemann-integrals-repetition-trig-integrals.pdf 143.1 KB
8. Norm, distance, angles, and orthogonality in inner product spaces/11.1 Slides_Cauchy--Schwarz inequality in the space of continuous functions.pdf 142.8 KB
11. Diagonalization of symmetric matrices/17.1 Article-Solved-Problems-Positive-Negative-Definite-Completing-the-Square.pdf 124.9 KB
7. Inner product as a generalization of dot product/1.1 Slides Between concrete and abstract.pdf 123.6 KB
9. Projections and Gram–Schmidt process in various inner product spaces/3.2 Slides_Why does normalizing work in the same way in all IP spaces.pdf 118.7 KB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/4.1 Article-SVD-theory.pdf 113.7 KB
11. Diagonalization of symmetric matrices/2.1 Slides_Some properties of symmetric matrices.pdf 100.1 KB

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