CAAM 335 · Matrix Analysis

Fall 2018 · Rice University


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Lectures

Lecture 42 (F 11/30): Review
Lecture 41 (W 11/28): Convergence of the PageRank algorithm
- Read Sections Page Rank Algorithm and Perron-Frobenius 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): Gram-Schmidt, QR Decomposition
- Read Section 6.4 of the Course Notes and Section Gram-Schmidt Orthogonalization and QR-Decomposition in the Supplemental Notes.
Lecture 25 (F 10/19): Gram-Schmidt Orthogonalization
- Read Section 6.4 of the Course Notes and Section Gram-Schmidt Orthogonalization and QR-Decomposition 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 4.1-4.3 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): LU-decomposition
- Read Sections 3.1, 3.2, pages 33-37 of the Course Notes and the LU-Decomposition 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 31-37 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 31-37 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 21-23 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 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 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 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 2 (W 8/22): Review of matrix-vector and matrix-matrix 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