udemy-linear-algebra-and-geometry-2-2021-8-3

–Schmidt process\ 1:59 Calculating projections, Problem 4 16:25 Calculating projections, Problem 5 25:20 Gram–Schmidt Process 36:06 Gram–Schmidt Process, Our unifying example 43:51 Gram–Schmidt Process, Problem 6 56:17 Gram–Schmidt Process, Problem 7 matrices\ 1:17:10 Product of a matrix and its transposed is symmetric 1:22:57 Definition and examples of orthogonal matrices 1:30:39 Geometry of 2-by-2 orthogonal matrices 1:37:57 A 3-by-3 example 1:44:51 Useful formulas for the coming proofs 1:52:34 Property 1_ Determinant of each orthogonal matrix is 1 or −1 2:00:04 Property 2_ Each orthogonal matrix A is invertible and A−1 is also orthogona 2:05:31 Property 3_ Orthonormal columns and rows 2:11:02 Property 4_ Orthogonal matrices are transition matrices between ON-bases 2:19:27 Property 5_ Preserving distances and angles 2:48:31 Property 6_ Product of orthogonal matrices is orthogonal 2:55:05 Orthogonal matrices, Problem 1 3:07:47 Orthogonal matrices, Problem 2 and eigenvectors\ 3:16:12 Crash course in factoring polynomials 3:35:41 Eigenvalues and eigenvectors, the terms 3:38:16 Order of defining, order of computing 3:40:14 Eigenvalues and eigenvectors geometrically 3:56:17 Eigenvalues and eigenvectors, Problem 1 4:01:31 How to compute eigenvalues Characteristic polynomial 4:18:40 How to compute eigenvectors 4:38:18 Finding eigenvalues and eigenvectors_ short and sweet 4:43:44 Eigenvalues and eigenvectors for examples from Video 180 5:17:42 Eigenvalues and eigenvectors, Problem 3 5:46:11 Eigenvalues and eigenvectors, Problem 4 5:59:14 Eigenvalues and eigenvectors, Problem 5 6:19:16 Eigenvalues and eigenvectors, Problem 6 6:49:19 Eigenvalues and eigenvectors, Problem 7 \ 6:57:40 Why you should love diagonal matrices 7:06:09 Similar matrices 7:09:19 Similarity of matrices is an equivalence relation (RST) 7:23:22 Shared properties of similar matrices 7:31:20 Diagonalizable matrices 7:35:59 How to diagonalize a matrix, a recipe 7:49:01 Diagonalize our favourite matrix 7:55:32 Eigenspaces; geometric and algebraic multiplicity of eigenvalues 8:10:02 Eigenspaces, Problem 2 8:40:21 Eigenvectors corresponding to different eigenvalues are linearly independent 9:05:59 A sufficient, but not necessary, condition for diagonalizability 9:08:53 Necessary and sufficient condition for diagonalizability 9:19:22 Diagonalizability, Problem 3 9:35:39 Diagonalizability, Problem 4 9:40:51 Diagonalizability, Problem 5 9:48:40 Diagonalizability, Problem 6 9:53:48 Diagonalizability, Problem 7 10:06:19 Powers of matrices 10:11:32 Powers of matrices, Problem 8 10:20:13 Diagonalization, Problem 9 10:30:18 Sneak peek into the next course; orthogonal diagonalization Linear Algebra and Geometry 2\ 10:36:10 Linear Algebra and Geometry 2, Wrap-up 10:43:47 Yes, there will be Part 3! 10:47:30 Final words