CAAM 335: Matrix Analysis
Instructor: Charles Puelz
Teaching Assistant: Sam Kroger
Location and Time: Monday, Wednesday, Friday, 2-250pm, Herzstein 210
(online on zoom for the beginning of the semester)
Office hours: Charles (Wednesday 3-4pm), Sam (Friday 3-4pm)
Recitation Session: Mondays 630-830pm in DCH 1070.
Syllabus: syllabus.pdf
Schedule and notes
- 8/25: vectors and operations (sections 1.1-1.2 of Cox). lecture-1-335.pdf
- 8/27: inner products, norms, and matrices (sections 1.1-1.2 of Cox). lecture-2-335.pdf
- 8/30: matrix operations (sections 1.1-1.2 of Cox). lecture-3-335.pdf
- 9/1: trace of a matrix and outer products. lecture-4-335.pdf
- 9/3: linear transformations and electrical circuit models (section 2.1 of Cox). lecture-5-335.pdf
- 9/8: linear systems for electrical circuit models. lecture-6-335.pdf
- 9/10: Householder reflectors and electrical circuits with batteries. lecture-7-335.pdf
- 9/13: Gaussian elimination. lecture-8-335.pdf
- 9/15: matrix inverses. lecture-9-335.pdf
- 9/17: matrix inverses (section 3.2 of Cox). lecture-10-335.pdf
- 9/20: intro to LU factorization (section 3.2 of Cox). lecture-11-335.pdf
- 9/22: LU and Cholesky factorizations (section 3.2 of Cox). lecture-12-335.pdf
- 9/24: planar truss example (section 3.3 of Cox). lecture-13-335.pdf
- 9/27: range, null space, and subspaces (section 4.1-4.3 of Cox). lecture-14-335.pdf
- 9/29: linear combinations and spans (section 4.1-4.3 of Cox). lecture-15-335.pdf
- 10/1: linear independence (section 4.1-4.3 of Cox). lecture-16-335.pdf
- 10/4: bases and dimension (section 4.1-4.3 of Cox). lecture-17-335.pdf
- 10/6: basis for the range of a matrix (section 4.1-4.3 of Cox). lecture-18-335.pdf
- 10/8: bases for null space and range (section 4.1-4.3 of Cox). lecture-19-335.pdf
- 10/13: fundamental theorem of linear algebra (FTLA) (section 5.1-5.2 of Cox). lecture-20-335.pdf
- 10/15: FTLA continued and intro to least squares. lecture-21-335.pdf
- 10/18: least squares via differentiation. lecture-22-335.pdf
- 10/20: least squares via FTLA (chapter 6 of Cox). lecture-23-335.pdf
- 10/22: geometry of the normal equations. lecture-24-335.pdf, least_squares_ex1.m, least_squares_ex2.m, least_squares_ex3.m
- 10/25: projections (section 6.3 of Cox). lecture-25-335.pdf
- 10/27: more on projections. lecture-26-335.pdf
- 10/29: Gram-Schmidt orthogonalization (section 6.4 of Cox). lecture-27-335.pdf
- 11/1: QR factorization (section 6.4 of Cox). lecture-28-335.pdf
- 11/3: determinants. lecture-29-335.pdf
- 11/5: lecture by Dan Lior on eigenvalues.
- 11/8: complex numbers. lecture-30-335.pdf
- 11/10: eigenvalues and eigenvectors. lecture-31-335.pdf
- 11/12: diagonalization. lecture-32-335.pdf
- 11/15: more on diagonalization and properties of eigenvalues/vectors. lecture-33-335.pdf
- 11/17: properties of eigenvalues/vectors. lecture-34-335.pdf
- 11/19: intro to the singular value decomposition. lecture-35-335.pdf
- 11/22: singular value decomposition. lecture-36-335.pdf
- 11/29: more SVD. lecture-37-335.pdf
- 12/1: SVD and linear least squares. lecture-38-335.pdf
- 12/3: regularized linear least squares. lecture-39-335.pdf
Homeworks
- homework 1. due 9/3. hw1_solutions.pdf.
- homework 2. due 9/17. hw2_solutions.pdf.
- homework 3. due 9/24. hw3_solutions.pdf.
- homework 4. due 10/4. hw4_solutions.pdf.
- homework 5. due 10/17. hw5_solutions.pdf.
- homework 6, fiber.m. due 10/29. hw6_solutions.pdf.
- homework 7, CAAM335HW7D1.mat, CAAM335HW7D2.mat. due 11/8. hw7_solutions.pdf.
- homework 8. due 11/17. hw8_solutions.pdf.
- homework 9. due 12/3. hw9_solutions.pdf.
- homework 10. (updated 12/7). due 12/14.
Supplemental material
- Linear algebra in Situ by Steve Cox.