Date |
Title |
Video |
Slides |
Wednesday, 9/6 |
Introduction |
Video
|
Slides
|
Friday, 9/8 |
The Field |
Video
|
Slides
|
Monday, 9/11 |
The Field (contd.) + The Vector |
Video
|
Slides
|
Wednesday, 9/13 |
The Vector (contd.) |
Video
|
Slides
|
Friday, 9/15 |
The Vector (contd.) |
Video
|
Slides
|
Monday, 9/18 |
The Vector Space |
Video
|
Slides
|
Wednesday, 9/20 |
The Vector Space (contd.) |
Video
|
Slides
|
Friday, 9/22 |
The Vector Space (contd.) |
Video
|
Slides
|
Monday, 9/25 |
The Vector Space, transition to The Matrix |
Video
|
Slides
|
Wednesday, 9/27 |
The Matrix |
Video
|
Slides
|
Friday, 9/29 |
The Matrix |
Video
|
Slides
|
Monday, 10/2 |
The Matrix, Error Correcting Codes |
Video
|
Slides
|
Wednesday, 10/4 |
Matrices, functions |
Video 1
Video 2
|
Slides
|
Friday, 10/6 |
Linear transformations and Matrix Inverses |
N/A |
Slides
|
Wednesday, 10/11 |
Coordinate representations, Grow and Shrink algorithm, representing graph edges with vectors |
Video
|
Slides
|
Friday, 10/13 |
Formulating minimum spanning forest in linear algebra; Linear dependence; Superfluous-Vector Lemma; Linear-Dependence Lemma |
Video
|
Slides
|
Monday, 10/16 |
Properties of linear (in)dependence; analyzing the grow & shrink algorithms; the basis |
Video
|
Slides
|
Wednesday, 10/18 |
Basis, unique representation, change of basis |
Video
|
Slides
|
Friday, 10/20 |
Wiimote whiteboard, Perspective rectification, start of Exchange Lemma |
Video
|
Slides
|
Monday, 10/23 |
Morphing Lemma, Dimension, Rank, Subset-Basis Lemma, Grow-Algorithm-Termination |
Video
|
Slides
|
Wednesday, 10/25 |
Superset-Basis Lemma, Dimension Lemma, Rank Theorem, Direct Sum |
Video
|
Slides
|
Friday, 10/27 |
Direct Sum, Invertibility of a Linear Function, Kernel-Image Theorem, Rank-Nullity Theorem |
Video
|
Slides
|
Monday, 10/30 |
Matrix invertibility, converting between representations of subspaces |
Video
|
Slides
|
Wednesday, 11/1 |
Interpretations of vector-matrix multiplication, Developing Gaussian elimination |
Video
|
Slides
|
Friday, 11/3 |
Gaussian Elimination: Recording the transformation, Algorithm for finding basis of null space |
Video
|
Slides
|
Monday, 11/6 |
Gaussian elimination, Integer factoring, Inner Product, Norm, Orthogonality |
Video
|
Slides
|
Wednesday, 11/8 |
Properties of orthogonality, parallel and perpendicular components of a vector, fire engine problem, computing the projections |
Video
|
Slides
|
Friday, 11/10 |
minimizing sum of squared distances, centroid, k-means, higher-dimensional projection, high-dimensional fire-engine lemma, projecting onto a higher-dimensional space |
Video 1
Video 2
|
Slides
|
Monday, 11/13 |
project onto (correct spec and proof of correctness), orthogonalization, nonzero orthogonal vectors are linearly independent |
Video
|
Slides
|
Wednesday, 11/15 |
matrix form for orthogonalize; computing a basis; find_subset_basis; basis for null space; orthogonal complement |
Video
|
Slides
|
Friday, 11/17 |
Null space and orthogonal complement; algorithm for computing orthogonal complement; normalization; orthonormal vectors; column-orthogonal and orthogonal matrices, QR factorization |
N/A |
Slides
|
Monday, 11/20 |
Using QR factorization to solve a matrix equation when the matrix has linearly independent columns; what if the columns are linearly dependent; the least-squares problem; using QR factorization to solve the least-squares problem when the matrix has linearly independent columns; the normal equations; linear regression; coping with approximate data (improving accuracy of output without more accurate measurements); applications of least squares when columns are linearly dependent |
Video
|
Slides
|
Monday, 11/27 |
The Singular Value Decomposition: Frobenius norm for matrices, low-rank matrices, the trolley-line-location problem, best rank-one approximation to a matrix |
Video
|
Slides
|
Friday, 12/1 |
Best rank-one approximation; Closest 1- and k- dimensional vector/affine space; The SVD: deriving it, its existence, its properties; Rank-k approximation in terms of the SVD |
Video
|
Slides
|
Monday, 12/4 |
Principal Component Analysis using SVD; Uses of SVD; Least squares using SVD |
Video
|
Slides
|
Wednesday, 12/6 |
Eigenvalues and Eigenvectors, similarity and diagonalizability, criterion for lambda being an eigenvalue of A, linearly independent eigenvectors, first look at power method |
Video
|
Slides
|
Friday, 12/8 |
Interpretation of eigenvalue analysis using change of basis; simple example of population dynamics; dance-floor dynamics and "forgetting" initial distribution; modeling spatial locality in CPU memory fetches; Markov chains; stationary distributions; power method; power method applied to a Markov chain; Perron-Frobenius Theorem; intro to Pagerank |
Video
|
Slides
|
Monday, 12/11 |
Pagerank (cont'd); Computing an eigenvalue; Limitations of eigenvector analysis; Eigenvalues for symmetric and asymmetric matrices; Positive definite, positive semi-definite, and determinant; Uses of determinants |
Video
|
Slides
|