| Date |
Video |
Slides |
| Wednesday, 9/3 |
Video |
See Friday, 9/5 |
| Friday, 9/5 |
Video |
The Field, part 1. Also see this note |
| Monday, 9/8 |
Video
|
The Field, part 2, The Vector (intro) |
| Wednesday, 9/10 |
Video |
The Vector (intro, continued) |
| Friday, 9/12 |
Video |
The Vector (remainder) |
| Monday, 9/15 |
Video |
The Vector Space (intro) |
| Wednesday, 9/17 |
Video |
The Vector Space (continued) |
| Friday, 9/19 |
Video |
The Matrix (intro) |
| Monday, 9/22 |
Video |
The Matrix (matrix-vector and vector-matrix multiplication) |
| Wednesday, 9/24 |
Video |
The Matrix (more dot-product uses, linear systems as matrix equations, coumn vectors and row vectors, algebraic properties of matrix-vector mult) |
| Friday, 9/26 |
Video |
The Matrix (Null space of a matrix, solution set of a matrix-vector equation, error-correcting codes, from function to matrix, linear functions) STILL ROUGH |
| Monday, 9/29 |
Video |
The Matrix (more on linear functions, kernel, one-to-one linear functions, the image, first look at onto linear functions) |
| Wednesday, 10/1 |
Video |
The Matrix (inner/outer products, matrix-mult and function composition, matrix inverse) |
| Friday, 10/3 |
Video |
The Basis (coordinate representations, greedy algorithms, minimum spanning forest) |
| Monday, 10/6 |
Video |
The Basis (superfluous-vector lemma, linear dependence, connection to other concepts, linear-dependence in MSF, properties of linear dependence, analyzing the Grow algorithm) |
| Wednesday, 10/8 |
Video |
The Basis (analyzing the Shrink Algorithm, intro to basis, intro to change of basis) |
| Friday, 10/10 |
Video |
The Basis (change of basis, cameras and perspective) |
| Monday, 10/13 |
No class |
| Wednesday, 10/15 |
Video |
The Basis (perspective rectification, Exchange Lemma) |
| Friday, 10/17 |
Video |
Dimension (The Morphing Lemma, Size of a Basis, rank and row rank and column rank, termination of Grow and Shrink) |
| Monday, 10/20 |
Video |
Dimension (Dimension Lemma, Rank Theorem, Direct Sum) |
| Wednesday, 10/22 |
Video |
Dimension (Direct-Sum Dimension Corollary, linear-function invertibility, extracting an invertible function), Oct. 22, 2014 |
| Friday, 10/24 |
Video |
Dimension (The Kernel-Image Theorem, linear function invertibility, the Rank-Nullity Theorem, matrix Invertibility, the Annihilator of a vector space), Oct. 24, 2014 |
| Monday, 10/27 |
Video |
Gaussian Elimination (Echelon form, multiplying by an invertible matrix preserves row space) |
| Wednesday, 10/29 |
Video |
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) |
| Friday, 10/31 |
Video |
Gaussian Elimination (recording transformations, factoring integers, authentication) |
| Monday, 11/3 |
Video |
The Inner Product (Fire-Engine Problem, norm, Inner product, orthogonality, project-along and project-orthogonal) |
| Wednesday, 11/5 |
Video |
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) |
| Friday, 11/7 |
Video |
Orthogonalization (loop invariant for project_orthogonal, augmented project_orthogonal, orthogonalization) |
| Monday, 11/10 |
Video |
Orthogonalization (matrix form, using orthogonalization for closest vector, basis, subset-basis, and null space basis) |
| Wednesday, 11/12 |
Video |
Orthogonalization (augmenting orthogonalize, matrices with mutually orthogonal columns, orthonormal vectors, QR factorization, solving Ax=b when A is invertible, least squares) |
| Friday, 11/14 |
Video |
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) |
| Monday, 11/17 |
Video |
The SVD (The trolley-line-location problem, first right singular vector and first singular value, visualizing high-dimensional data on a line) |
| Wednesday, 11/19 |
Video |
The SVD (Best rank-one approximation to a matrix, closest one-dimensional affine space, closest k-dimensional vector space, closest k-dimensional affine space) |
| Friday, 11/21 |
Partial video (initial part of lecture not recorded) |
The SVD (SVD existence proof, best rank-k approximation, in terms of SVD, two principal components, function interpretation of SVD, least squares via SVD) |
| Monday, 11/24 |
Video |
The SVD (simple example of deblurring), The Eigenvector (two interest-bearing accounts, Fibonacci numbers, definition of eigenvalues and eigenvectors) |
| Wednesday, 11/26 |
Thanksgiving |
| Friday, 11/28 |
Thanksgiving |
| Monday, 12/2 |
Video |
The Eigenvector (Eigenvalues and invertibility, similarity between matrices, diagonalizability, diagonalizable matrices and change of basis, sick rabbits) |
| Wednesday, 12/3 |
To Be Posted |
The Eigenvector (The Worm, The Dance Club, Randy, first look at stationary distribution, Markov chains, spatial locality in CPU memory fetches, Markov chains)
|
| Friday, 12/5 |
Video |
The Eigenvector (Stationary distribution, Perron-Frobenius Theorem implication, Power method, Pagerank) |
| Monday, 12/9 |
Video |
The Eigenvector (Proof of existence of eigenvalues, computing an eigenvalue) |
| Wednesday, 12/10 |
Video |
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) |
