Previously: 2016

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