CAAM 335 · Matrix AnalysisFall 2018 · Rice University

Lecture 42 (F 11/30):  Review 
Lecture 41 (W 11/28):  Convergence of the PageRank algorithm  Read Sections Page Rank Algorithm and PerronFrobenius Theorem in the Supplemental Notes. 
Lecture 40 (M 11/26):  The Singular Value Decomposition (SVD) and classification  Read Chapter 13 of the course notes and Section\ SVD and Classification in the Supplemental Notes.  Matlab code for classification of handwritten digits digit_classify.m. 
(F 11/23):  Thanksgiving break 
Lecture 39 (W 11/21):  The Singular Value Decomposition (SVD) and data compression  Read Chapter 13 of the course notes and Section SVD and Data Compression\ in the Supplemental Notes.  Matlab code for image compression via the SVD implot.m. 
Lecture 38 (M 11/19):  The Singular Value Decomposition (SVD) and
the solution of regularized linear least squares problems  Read Chapter 13 of the course notes and Section Regularized Linear Least Squares Problems and the SVD in the Supplemental Notes.  Matlab code for regularized linear least squares via SVD lls_pert_reg.m and initial_cond_est.m. 
Lecture 37 (F 11/16):  The Singular Value Decomposition (SVD),
the Fundamental Theorem of Linear Algebra, and
the solution of linear least squares problems  Read Chapter 13 of the course notes and Section The Singular Value Decomposition in the Supplemental Notes.  Matlab code for linear least squares via SVD lls_pert.m. 
Lecture 36 (W 11/14):  The Singular Value Decomposition (SVD)  Read Chapter 13 of the Course Notes and Section The Singular Value Decomposition in the Supplemental Notes. 
Lecture 35 (M 11/12):  The Jordan Normal Form  Read Section The Jordan Normal Form in the Supplemental Notes.  Matlab code for the reaction system reaction_ode_eig.m. 
Lecture 34 (F 11/9):  Dynamical systems: Application to mechanical systems Read Section Dynamical Systems: Mechanical Systems in the Supplemental Notes.  Matlab: spring_ode.m 
Lecture 33 (W 11/7):  Diagonalization of matrices and the solution of dynamical systems  Read Section Diagonalization of Matrices and the Solution of Dynamical Systems in the Supplemental Notes.  Matlab: dyn_sys_ex.m 
Lecture 32 (M 11/5):  Diagonalization of symmetric matrices; solution of linear systems;
pseudo inverse  Read Sections Diagonalization of Symmetric Matrices and Diagonalization of Matrices and the Solution of Linear Systems in the Supplemental Notes. 
Lecture 31 (F 11/2):  Diagonalization of symmetric matrices  Read Section Diagonalization of Symmetric Matrices in the Supplemental Notes. 
Lecture 30 (W 10/31):  Basic properties of eigenvalues and eigenvectors Read Sections Section Basic Properties of Eigenvectors and Eigenvalues in the Supplemental Notes. 
Lecture 29 (M 10/29):  Overview of eigenvalues and eigenvectors; properties of eigenvalues and eigenvectors Read Sections Sections Overview of Eigenvectors and Eigenvalues and Eigenvectors and Eigenvalues in the Supplemental Notes. 
Lecture 28 (F 10/26):  Dynamical systems. Read Sections Dynamical Systems and Overview of Eigenvectors and Eigenvalues in the Supplemental Notes. 
Lecture 27 (W 10/24):  Complex Numbers  Read Section 9.1 of the course notes.  Read Section Complex Numbers in the Supplemental Notes. 
Lecture 26 (M 10/22):  GramSchmidt, QR Decomposition  Read Section 6.4 of the Course Notes and Section GramSchmidt Orthogonalization and QRDecomposition in the Supplemental Notes. 
Lecture 25 (F 10/19):  GramSchmidt Orthogonalization  Read Section 6.4 of the Course Notes and Section GramSchmidt Orthogonalization and QRDecomposition in the Supplemental Notes. 
Lecture 24 (W 10/17):  Projections  Read Section 6.3 in the Course Notes and the Projections section in the Supplemental Notes. 
Lecture 23 (M 10/15):  Applications of Linear Least Squares Problems; Projections  Read Section 6.2 in the Course Notes and the Linear Least Squares section in the Supplemental Notes.  MATLAB demo: findfiber.m 
Lecture 22 (F 10/12):  Applications of Linear Least Squares Problems  Read Section 6.2 in the Course Notes and the Linear Least Squares section in the Supplemental Notes.  MATLAB demo: findfiber.m 
Lecture 21 (W 10/10):  Linear Least Squares Problems  Read Sections 6.1 and 6.2 in the Course Notes and the Linear Least Squares section in the Supplemental Notes. 
(M 10/8):  Fall Recess 
Lecture 20 (F 10/5):  Vector Spaces and Linear Transformations  Read Section 5.3 in the Course Notes and the Vector Space section in the Supplemental Notes. 
Lecture 19 (W 10/3):  Vector Spaces and Linear Transformations  Read Section 5.3 in the Course Notes and the Vector Space section in the Supplemental Notes.  MATLAB demo: bvp_FEM.m. 
Lecture 18 (M 10/1):  Vector Spaces and Linear Transformations  Read Section 5.3 in the Course Notes and the Vector Space section in the Supplemental Notes. 
Lecture 17 (F 9/28):  Fundamental Theorem of Linear Algebra: Application to Trusses  Read Sections 5.1 and 5.2 in the Course Notes and the Fundamental Theorem of Linear Algebra section in the Supplemental Notes. 
Lecture 16 (W 9/26):  Fundamental Theorem of Linear Algebra  Read Sections 5.1 and 5.2 in the Course Notes and the Fundamental Theorem of Linear Algebra section in the Supplemental Notes. 
Lecture 15 (M 9/24):  Basis and Dimension of a Subspace  Read Section 4.3 in the Course Notes, and the Range and Null Space section in the Supplemental Notes. 
Lecture 14 (F 9/21):  Basis of a subspace, computing bases of the column space and of the null space  Read Sections 4.14.3 in the Course Notes and the Range and Null Space section in the Supplemental Notes. 
Lecture 13 (W 9/19):  The column space and the null space  Read Sections 4.1 and 4.2 in the Course Notes and the Range and Null Space section in the Supplemental Notes. 
Lecture 12 (M 9/17):  Planar truss  Read Section 3.3 in the Course Notes and the Planar Trusses section in the Supplemental Notes.  MATLAB demos: fiber.m for the 3x3 tissue in Figure 3.5  MATLAB demos: truss.m, stiff.m for the truss in the supplemental notes. transmission_tower.m.  MATLAB demo driver_bracket_truss_optim_lp.m for a structural optimization problem. 
Lecture 11 F 9/14 ):  Simple planar truss; existence of solutions, null space of A  Read Section 3.3 in the Course Notes and the Planar Trusses section in the Supplemental Notes.  MATLAB demos: fiber.m for the 3x3 tissue in Figure 3.5 
Lecture 10 (W 9/12):  Existence of the matrix inverse; simple planar truss  Read Section 3.3 in the Course Notes and the Matrix Inverse section in the Supplemental Notes. 
Lecture 9 (M 9/10):  LUdecomposition  Read Sections 3.1, 3.2, pages 3337 of the Course Notes and the LUDecomposition section in the Supplemental Notes. 
Lecture 8 (F 9/7):  Computation of the matrix inverse; determinant
of a matrix  Read Sections 3.1, 3.2, pages 3137 of the Course Notes and the Matrix Inverse and Determinant sections in the Supplemental Notes. 
Lecture 7 (W 9/5):  Gaussian elimination; matrix inverse  Read Sections 3.1, 3.2, pages 3137 in the Course Notes and the Gaussian Elimination section in the Supplemental Notes. 
(M 9/3):  Labor Day; Rice closed. 
Lecture 6 (F 8/31):  Networks with resistors and batteries; matrix model of a mass spring system  Read Chapter 2, pages 2123 in the Course Notes and the Electrical Circuits section in the Supplemental Notes.  Read Chapter 3.1, pages 31, 32 in the Course Notes.  MATLAB demos: fib2.m and ladder.m. Additional reading:  Matrix Analysis of the Branched Dendrite Nerve Fiber. 
Lecture 5 (W 8/29):  Matrix models of resistor networks  Read Chapter 2, pages 19+20 of the Course Notes and the Electrical Circuits section in the Supplemental Notes.  MATLAB demo fib1.m. 
Lecture 4 (M 8/27):  Google PageRank  Read the Google PageRank section in the Supplemental Notes.  MATLAB demo pagerank_demo1.m. Additional reading:  Chapter 7 Google PageRank in Cleve Moler's Ebook Experiments with MATLAB and the corresponding MATLAB code (click on the Functions tab and look for pagerank).  The original papers The anatomy of a largescale 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 3 (F 8/24):  Review of matrix operations Google PageRank  Read the Google PageRank section in the Supplemental Notes.  MATLAB demo pagerank_demo1.m. Additional reading:  Chapter 7 Google PageRank in Cleve Moler's Ebook Experiments with MATLAB and the corresponding MATLAB code (click on the Functions tab and look for pagerank).  The original papers The anatomy of a largescale 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 2 (W 8/22):  Review of matrixvector and matrixmatrix multiplication  Read Chapter 1 of the Course Notes. 
Lecture 1 (M 8/20):  Course overview;
review of vectors, basic operations, norms.  Read Chapter 1 of the Course Notes 