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product as a generalization of dot product\ 1:03 Frobenius inner product; Hadamard product of matrices , distance, angles, and orthogonality in inner product spaces\ 14:35 Norm in inner product spaces 27:40 Weird geometry in the Euclidean space with weighted inner product 34:52 Frobenius norm of matrices, Problem 1 40:55 Norm in the space of functions, Problem 2 48:09 Distance in inner product spaces 55:55 Frobenius distance between matrices, Problem 3 1:01:54 Distance in the space of functions, Problem 4 1:09:21 First step to defining abstract angles 1:14:31 Cauchy–Schwarz inequality, proof 1 1:40:43 Cauchy–Schwarz inequality, proof 2 2:03:58 Cauchy–Schwarz inequality in the space of continuous functions 2:08:18 Angles in inner product spaces 2:12:33 More weird geometry Angles in inner product spaces, Problem 5 2:20:30 Angles in inner product spaces, Problem 6 2:24:31 Orthogonality in inner product spaces 2:28:27 Orthogonality in inner product spaces depends on inner product 2:34:43 Orthogonality in inner product spaces, Problem 7 2:41:21 What is triangle inequality 2:51:43 Triangle inequality in inner product spaces 3:10:23 Generalized Theorem of Pythagoras 3:18:27 Generalized Theorem of Pythagoras, Problem 8 3:29:29 Generalized Theorem of Pythagoras, Problem 9 3:37:17 Generalized Theorem of Pythagoras, Problem 10 and Gram–Schmidt process in various inner product spaces\ 3:55:45 Different but still awesome! 3:59:38 ON bases in IP spaces 4:05:18 Why does normalizing work in the same way in all IP spaces 4:11:21 Orthonormal sets of continuous functions, Problem 1 4:42:49 Orthogonal complements, Problem 2 4:58:35 Orthogonal sets are linearly independent, Problem 3 5:08:02 Coordinates in orthogonal bases in IP spaces 5:11:29 Projections and orthogonal decomposition in IP spaces 5:23:18 Orthogonal projections on subspaces of an IP space, Problem 4 5:47:10 Orthogonal projections on subspaces of an IP space, Problem 5 6:04:59 Gram–Schmidt in IP spaces 6:10:22 Gram–Schmidt in IP spaces, Problem 6 Legendre polynomials 6:23:41 Gram–Schmidt in IP spaces, Problem 7 6:48:16 Easy computations of IP in ON bases, Problem 8 problems, best approximations, and least squares\ 7:02:49 In this section 7:12:05 Min-max, Problem 1 7:34:13 Min-max, Problem 2 7:45:34 Min-max, Problem 3 7:54:24 Min-max, Problem 4 8:12:16 Min-max, Problem 5 8:30:21 Another look at orthogonal projections as matrix transformations 8:48:50 Orthogonal projections, Problem 6 8:57:16 Orthogonal projections, Problem 7 9:01:30 Shortest distance from a subspace 9:15:12 Shortest distance, Problem 8 9:20:37 Shortest distance, Problem 9 9:32:09 Shortest distance, Problem 10 9:36:05 Solvability of systems of equations in terms of the column space 9:42:21 Least squares solution and residual vector 9:47:38 Four fundamental matrix spaces and the normal equation 10:05:11 Least squares, Problem 11, by normal equation 10:23:47 Least squares, Problem 11, by projection 10:40:57 Least squares straight line fit, Problem 12 11:05:04 Least squares, fitting a quadratic curve to data, Problem 13 of symmetric matrices\ 11:17:13 The link between symmetric matrices and quadratic forms, Problem 1 11:40:40 Some properties of symmetric matrices 11:45:33 Eigenvectors corresponding to distinct eigenvalues for a symmetric matrix 11:59:43 Complex numbers a brief repetition
