# CAAM 335 · Matrix Analysis

## Spring 2018 · Rice University

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## Lectures

 Lecture 39 (F 4/20): Semester review and recap. Lecture 38 (W 4/18): Singular value decomposition (SVD), cont: applications in classification. Supplementary notes ("The SVD and classification") Lecture 37 (M 4/16): Singular value decomposition (SVD), cont: applications in data analysis. Supplementary notes ("The SVD and data compression") SVD congressional demos and data. Lecture 36 (W 4/13): Singular value decomposition (SVD), cont: low rank approximations and data compression, cont. Supplementary notes ("The SVD and data compression") supreme_court.mat: SVD of Supreme court voting patterns Lecture 35 (W 4/11): Singular value decomposition (SVD), cont: low rank approximations and data compression Supplementary notes ("The SVD and data compression") implot.m: SVD for image compression Images to test: Mondrian, Rothko, Kline. Lecture 34 (M 4/9): Singular value decomposition (SVD), cont: least squares problems, fundamental theorem of linear algebra Supplementary notes ("The Singular Value Decomposition", "The SVD and the Fundamental Theorem of Linear Algebra", "Linear least squares problems and the SVD") Lecture 33 (F 4/6): Singular value decomposition (SVD) Supplementary notes ("The Singular Value Decomposition") Lecture 32 (W 4/4): Matrix exponentials using the Jordan normal form, singular value decomposition (SVD) Supplementary notes ("Jordan normal form", "Computing the matrix exponential using the Jordan normal form", "The Singular Value Decomposition") Lecture 31 (M 4/2): Jordan normal form Supplementary notes ("Jordan normal form") Lecture 30 (F 3/30): Solution of systems of ODEs, exam 2 review, Jordan normal form Supplementary notes ("Diagonalization of Matrices and the Solution of Dynamical Systems", "Jordan normal form") Matlab demo of damped spring system. Needs extra springcoord.m file to run. Lecture 29 (W 3/28): Solution of systems of ODEs using the eigenvalue decomposition. Supplementary notes ("Diagonalization of Matrices and the Solution of Dynamical Systems") Matlab demo of several ODE systems. Matlab demo of spring system. Needs extra springcoord.m file to run. Lecture 28 (M 3/26): Solution of systems using the eigenvalue decomposition. Supplementary notes ("Diagonalization of matrices and the solution of linear systems") Lecture 27 (F 3/23): Eigenvalues and eigenvectors for symmetric matrices, solution of systems using the eigenvalue decomposition. Supplementary notes ("Diagonalization of symmetric matrices", "Diagonalization of matrices and the solution of linear systems") Lecture 26 (W 3/21): Properties of eigenvalues and eigenvectors. Supplementary notes ("Basic properties of eigenvalues and eigenvectors") Lecture 25 (M 3/19): Eigenvalues and eigenvectors, cont. Supplementary notes ("Basic properties of eigenvalues and eigenvectors") Lecture 24 (F 3/9): Introduction to eigenvalues and eigenvectors Supplementary notes ("Overview of eigenvalues and eigenvectors") Lecture 23 (W 3/7): Dynamical systems Supplementary notes ("Dynamical systems") Lecture 22 (M 3/5): Complex numbers Section 9.1 in the course notes, Supplementary notes ("Complex Numbers") Lecture 21 (F 3/2): QR factorization and least squares, Householder transformations. Chapter 6, sections 6.2, 6.4 in the Course Notes, Supplementary notes ("Gram-Schmidt Orthogonalization and QR-Decomposition") Code: least squares using QR and QR via Householder transforms. Lecture 20 (W 2/28): Gram-Schmidt orthogonalization and QR factorization. Chapter 6, sections 6.2, 6.4 in the Course Notes, Supplementary notes ("Gram-Schmidt Orthogonalization and QR-Decomposition") Lecture 19 (M 2/26): Least squares examples, Gram-Schmidt orthogonalization. Chapter 6, sections 6.2, 6.4 in the Course Notes, Supplementary notes ("Gram-Schmidt Orthogonalization and QR-Decomposition") Code for using least squares to recover a stiff fiber. Lecture 18 (F 2/23): Least squares examples and projection matrices. Chapter 6, sections 6.1, 6.2, 6.3 in the Course Notes, Supplementary notes ("Examples of linear least squares problem", "Projections") Code for fitting a circle. Lecture 17 (W 2/21): Least squares problems: examples. Chapter 6, sections 6.1 and 6.2 in the Course Notes, Supplementary notes ("Linear least squares problem") Code for fitting a circle. Lecture 16 (M 2/19): Least squares problems. Chapter 6, sections 6.1 and 6.2 in the Course Notes, Supplementary notes ("Linear least squares problem") Code for linear regression. Lecture 15 (F 2/16): Vector spaces and linear transformations. Supplementary notes ("Vector spaces", subsection "Linear Transformations") Lecture 14 (W 2/14): Fundamental theorem; vector spaces. Supplementary notes ("Fundamental Theorem of Linear Algebra", "Vector spaces") Lecture 13 (M 2/12): The fundamental theorem of linear algebra. Chapter 5 (sections 5.1-5.2) and supplementary notes ("Fundamental Theorem of Linear Algebra") Lecture 12 (W 2/7): Computing bases for range and null spaces, dimensions of subspaces. Chapter 4 (sections 4.1-4.3) and supplementary notes ("Range Space and Null Space of a Matrix") Lecture 11 (M 2/5): Range and null spaces, span and basis. Chapter 4 (sections 4.1-4.2) and supplementary notes ("Range Space and Null Space of a Matrix") Lecture 10 (F 2/2): More complex planar trusses and null spaces. Chapter 3 (sections 3.3) and supplementary notes ("Planar Trusses", "Range Space and Null Space of a Matrix") Codes: 3x3 fiber code (fiber.m), truss codes (truss.m and stiff.m). Lecture 9 (W 1/31): Planar trusses, singular matrices. Chapter 3 (sections 3.3) and supplementary notes ("Planar Trusses") Lecture 8 (M 1/29): Review of LU factorization, theory on matrix inverse. Chapter 3 (sections 3.1-3.3) and supplementary notes ("Matrix Inverse") Lecture 7 (F 1/26): Matrix inverse, LU factorization, determinant. Chapter 3 (sections 3.1-3.3) and supplementary notes ("Matrix Inverse" and "Determinant" sections) Lecture 6 (W 1/24): Gaussian elimination, matrix inverse. Chapter 3 (sections 3.1, 3.2) Lecture 5 (M 1/22): Electrical networks with batteries, mass-spring networks Chapter 2 fib2.m Code for electrical networks with batteries Lecture 4 (F 1/19): Electrical networks, compartment models of neurons Chapter 2 fiber_demo.m (3-compartment case in class) fib1.m (multi-compartment case) Cancelled (W 1/17): Icy roads (stay warm) Holiday (M 1/15): MLK day Lecture 3 (F 1/12): Google PageRank - Supplemental notes on PageRank - 6-website PageRank demo from clas pageRankExample.m. - MATLAB demo pagerank_demo1.m. Additional reading: - Chapter 7 Google PageRank in Cleve Moler's E-book Experiments with MATLAB and the corresponding MATLAB code (click on the Functions tab and look for pagerank). - The original papers The anatomy of a large-scale hypertextual Web search engine by S. Brin and L. Page, and The PageRank Citation Ranking: Bringing Order to the Web by L. Page, S. Brin, R.Motwani, and T. Winograd. Lecture notes Lecture 2 (W 1/10): Matrix-vector and matrix-matrix multiplication Supplemental notes on matrix multiplicaton Chapter 1. Lecture 1 (M 1/8): Course overview; vectors, basic operations, norms. Chapter 1.