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Coding the Matrix, Fall 2014 Philip Klein cs053ta

Videos

Thumbnail The Eigenvector (Limitations of eigenvalue analysis, eigenvalues for symmetric matrices, complex conjugate, Hermitian, eigenvalues and eigenvectors of symmetric matrices, relating singular values to eigenvalues, estimating a right singular vector using the power method, deflation), Dec. 10, 2014 0:36:29 Philip Klein cs053ta Coding the Matrix, Fall 2014

Thumbnail The Eigenvector (Proof of existence of eigenvalues, computing an eigenvalue), Dec. 8, 2014 0:35:36 Philip Klein cs053ta Coding the Matrix, Fall 2014

Thumbnail The Eigenvector (Stationary distribution, Perron-Frobenius Theorem implication, Power method, Pagerank), Dec. 5, 2014 0:48:55 Philip Klein cs053ta Coding the Matrix, Fall 2014

Thumbnail The Eigenvector (The Worm, The Dance Club, Randy, first look at stationary distribution, Markov chains, spatial locality in CPU memory fetches, Markov chains), Dec. 3, 2014 0:47:20 Philip Klein cs053ta Coding the Matrix, Fall 2014

Thumbnail The Eigenvector (Eigenvalues and invertibility, similarity between matrices, diagonalizability, diagonalizable matrices and change of basis, sick rabbits), Dec. 1, 2014 0:48:50 Philip Klein cs053ta Coding the Matrix, Fall 2014

Thumbnail The SVD (simple example of deblurring), The Eigenvector (two interest-bearing accounts, Fibonacci numbers, definition of eigenvalues and eigenvectors), Nov. 24, 2014 0:35:34 Philip Klein cs053ta Coding the Matrix, Fall 2014

Thumbnail The SVD (SVD existence proof, best rank-k approximation, in terms of SVD, two principal components, function interpretation of SVD, least squares via SVD), Nov. 21, 2014 0:38:11 Philip Klein cs053ta Coding the Matrix, Fall 2014

Thumbnail The SVD (Best rank-one approximation to a matrix, closest one-dimensional affine space, closest k-dimensional vector space, closest k-dimensional affine space), Nov. 19, 2014 0:48:52 Philip Klein cs053ta Coding the Matrix, Fall 2014

Thumbnail The SVD (The trolley-line-location problem, first right singular vector and first singular value, visualizing high-dimensional data on a line), Nov. 17, 2014 0:43:12 Philip Klein cs053ta Coding the Matrix, Fall 2014

Thumbnail Orthogonalization (least squares, linear regression, compensating for inaccurate measurements by using more measurements, applying least-squares to the machine-learning problem), The SVD (multiplying a vector by a rank-one or low-rank matrix, Frobenius norm), Nov. 14, 2014 0:44:12 Philip Klein cs053ta Coding the Matrix, Fall 2014

Thumbnail Orthogonalization (augmenting orthogonalize, matrices with mutually orthogonal columns, orthonormal vectors, QR factorization, solving Ax=b when A is invertible, least squares), Nov. 12, 2014 0:48:21 Philip Klein cs053ta Coding the Matrix, Fall 2014

Thumbnail Orthogonalization (matrix form, using orthogonalization for closest vector, basis, subset-basis, and null space basis), Nov. 10, 2014 0:59:42 Philip Klein cs053ta Coding the Matrix, Fall 2014

Thumbnail Orthogonalization (loop invariant for project_orthogonal, augmented project_orthogonal, orthogonalization), Nov. 7, 2014 0:49:49 Philip Klein cs053ta Coding the Matrix, Fall 2014

Thumbnail Orthogonalization (closest point in a plane, closest point in a vector space, high-dimensional fire-engine lemma, projection onto V, projection orthogonal to V, project_orthogonal), Nov. 5, 2014 0:46:01 Philip Klein cs053ta Coding the Matrix, Fall 2014

Thumbnail The Inner Product (Fire-Engine Problem, norm, Inner product, orthogonality, project-along and project-orthogonal), Nov. 3, 2014 0:49:32 Philip Klein cs053ta Coding the Matrix, Fall 2014

Thumbnail Gaussian Elimination (recording transformations, factoring integers, authentication), Oct. 31, 2014 0:46:43 Philip Klein cs053ta Coding the Matrix, Fall 2014

Thumbnail Gaussian Elimination (Using elementary row-addition operations, failure of Gaussian elimination, Gaussian elimination over GF(2), using Gaussian elimination for solving a linear system and for finding a basis for the null space), Oct. 30, 2014 0:31:09 Philip Klein cs053ta Coding the Matrix, Fall 2014

Thumbnail Gaussian Elimination (Echelon form, multiplying by an invertible matrix preserves row space), Oct. 27, 2014 0:29:08 Philip Klein cs053ta Coding the Matrix, Fall 2014

Thumbnail Dimension (The Kernel-Image Theorem, linear function invertibility, the Rank-Nullity Theorem, matrix Invertibility, the Annihilator of a vector space), Oct. 24, 2014 0:47:14 Philip Klein cs053ta Coding the Matrix, Fall 2014

Thumbnail Dimension (Direct-Sum Dimension Corollary, linear-function invertibility, extracting an invertible function), Oct. 22, 2014 0:49:59 Philip Klein cs053ta Coding the Matrix, Fall 2014

Thumbnail Dimension (Dimension Lemma, Rank Theorem, Direct Sum), Oct. 20, 2014 0:46:18 Philip Klein cs053ta Coding the Matrix, Fall 2014

Thumbnail Dimension (The Morphing Lemma, Size of a Basis, rank and row rank and column rank, termination of Grow and Shrink), Oct. 17, 2014 0:44:02 Philip Klein cs053ta Coding the Matrix, Fall 2014

Thumbnail The Basis (perspective rectification, Exchange Lemma), Oct. 15, 2014 0:37:11 Philip Klein cs053ta Coding the Matrix, Fall 2014

Thumbnail The Basis (change of basis, cameras and perspective) 0:39:00 Philip Klein cs053ta Coding the Matrix, Fall 2014

Thumbnail The Basis (analyzing the Shrink Algorithm, intro to basis, intro to change of basis), Oct. 8, 2014 0:48:37 Philip Klein cs053ta Coding the Matrix, Fall 2014

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