udemy-linear-algebra-and-geometry-3-2021-10-0

\ 0:00 Introduction operators in the plane and in the 3-space\ 19:30 Eigendecomposition, recap 42:14 Eigendecomposition and operators 50:23 Problem 1 Line symmetry in the plane 1:05:05 Problem 2 Projection in the plane 1:17:51 Problem 3 Symmetry in the 3-space 1:40:31 Problem 4 Projection in the 3-space 2:11:31 Problem 5 Projection in the 3-space 2:41:58 Another formulation of eigendecomposition Spectral decomposition 3:08:46 Powers of matrices Two methods 3:28:40 Spectral decomposition, Problem 6 3:45:54 Spectral decomposition, Problem 7 4:14:09 Spectral decomposition, Geometrical illustration, Problem 8 problem solving; spaces different from R^n\ 4:44:59 Eigendecomposition, Problem 1 5:31:35 Eigendecomposition, Problem 2 6:01:33 Powers and roots, Problem 3 6:32:59 Powers and roots, Problem 4 7:11:38 In the space of polynomials, Problem 5 8:07:35 In the space of polynomials, Problem 6 8:25:02 In the space of matrices, Problem 7 isomorphic vector spaces\ 8:52:13 You wouldn’t see the difference 9:04:34 Different spaces with the same structure 9:22:07 More examples of isomorphic vector spaces 9:30:22 A necessary condition for isomorphic vector spaces 9:56:41 A necessary and sufficient condition for isomorphic vector spaces 10:05:30 Why you don’t see the difference 10:18:21 Isomorphic spaces Problem 1 10:26:45 Isomorphic spaces Problem 2 10:35:24 Isomorphic spaces Problem 3 10:57:02 Vector spaces, fields, rings; ring homomorphisms and isomorphisms 11:18:26 Vector spaces, fields, rings, Problem 4 11:42:32 Vector spaces, fields, rings, Problem 5