udemy-linear-algebra-and-geometry-3-2021-10-3

of symmetric matrices\ 16:23 Eigenvalues for a (real) symmetric matrix are real 47:13 Orthogonal diagonalization 53:33 If a matrix is orthogonally diagonalizable, it is symmetric 57:42 The Spectral Theorem Each symmetric matrix is orthogonally diagonalizable 1:12:52 Orthogonal diagonalization how to do it 1:18:56 Orthogonal diagonalization, Problem 2 1:28:33 Spectral decomposition for symmetric matrices, Problem 3 1:54:28 Orthogonal diagonalization, Problem 4 2:14:00 Orthogonal diagonalization, Problem 5 2:19:55 Orthogonal diagonalization, Problem 6 2:34:18 Orthogonal diagonalization, Problem 7 2:40:05 Spectral decomposition, Problem 8 2:55:04 Pos and neg definite matrices, semidefinite and indefinite matrices, Problem 9 3:29:10 The wonderful strength of an orthogonally diagonalized matrix 3:40:13 Three tests for definiteness of symmetric matrices, Problem 10 3:55:56 Symmetric square roots of symmetric positive definite matrices; singular values forms and their classification\ 4:07:05 The correspondence between quadratic forms and symmetric matrices is 1-to-1 4:30:56 Completing the square is not unique 4:37:43 What kind of questions we want to answer 4:46:28 163 Quadratic forms in two variables, Problem 1. 4:56:37 Quadratic forms in two variables, Problem 2 5:07:48 Quadratic curves, generally 5:16:14 Quadratic curves as conic sections 5:27:27 Quadratic curves by distances; shortest distance from the origin 5:47:03 Principal axes; The shortest distance from the origin, Problem 3 6:08:30 Classification of quadratic forms in two variables 6:18:49 Classification of curves, Problem 4 6:35:35 Classification of curves, Problem 5 6:47:25 Different roles of symmetric matrices (back to Videos 150 and 168), Problem 7:12:45 Classification of curves, Problem 7 7:26:38 Generally about quadratic surfaces 7:44:39 Some nice visuals on quadratic surfaces 8:02:38 Quadratic surfaces, shortest distance, Problem 8 8:31:26 Quadratic surfaces, Problem 9 8:46:37 Quadratic surfaces, Problem 10 9:03:45 Law of inertia for quadratic forms; Signature of a form, Problem 11 9:31:20 Four methods of determining definiteness; Problem 12 optimization\ 9:44:14 The theory for this section 10:14:44 Constrained optimization, Problem 1 10:20:57 Constrained optimization, Problem 2 10:27:06 Constrained optimization, Problem 3 10:32:42 Constrained optimization, Problem 4 Grand Finale Singular Value Decomposition and Pseudoinverses\ 10:36:10 All our roads led us to SVD 10:38:19 Why do we need SVD 10:44:43 We know really a lot about AT A for any rectangular matrix A 10:53:28 New facts about AT A eigenvalues and eigenvectors Singular values of A 11:10:19 ON-bases containing only eigenvectors of certain matrix products 11:33:27 Singular value decomposition with proof and geometric interpretation