CAAM 335 · Matrix Analysis

Spring 2018 · Rice University


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Lectures


Lecture 18 (W 2/23): Least squares examples and projection matrices.
Chapter 6, sections 6.1 and 6.2 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.