Text: Gilbert Strang, Linear Algebra and its Applications,
Fourth Edition (New Edition)
ISBN 0-03-010567-6, Thomson -- Brooks/Cole, 2006.
| Date | Lecture | Reading | Topics |
|---|---|---|---|
| 9/7 | 1 | 1.4-5 | Review of Matrix Algebra; Gaussian Elimination by Elementary Matrices |
| 9/12 | 2 | 1.6 | LU and LDU Factorizations; Matrix Inverses |
| 9/14 | 3 | 2.1-2 | Vector Spaces and Subspaces; Solving Linear Systems |
| 9/19 | 4 | 2.3-4 | Linear Independence, Basis, and Dimension; Four Fundamental Subspaces |
| 9/21 | 5 | 2.6 | Linear Transformations and Their Matrices |
| MATLAB Assignment # 1 due 9/26 | |||
| 9/26 | 6 | 3.1-2 | Orthogonal Spaces; Inner Products and Projections |
| 9/28 | 7 | 3.3 | Projections and Least-squares Approximations |
| 10/3 | 8 | 3.4 | Orthonormal Bases; Gram-Schmidt Process; QR Factorization |
| 10/5 | 9 | 4.1-2 | Properties of the Determinant Function |
| 10/10 | 10 | 4.2-3 | Formulas for Determinants; Permutations |
| 10/12 | 11 | 4.4 | Determinant Formulas for Matrix Inverse; Cramer's Rule |
| MATLAB Assignment # 2 due 10/17 | |||
| 10/17 | 12 | 5.1-2 | Eigenvalues and Eigenvectors; Diagonalization |
| 10/19 | 13 | 5.3-4 | Difference and Differential Equations |
| 10/24 | 14 | Midterm Exam on Chapters 1-4 (closed book) | |
| 10/26 | 15 | 5.4, 5.5 | Matrix Exponentials; Complex vector spaces; Hermitian matrices |
| 10/31 | 16 | 5.6 | Schur Triangular Form; Unitary Diagonalization of Normal Matrices |
| 11/2 | 17 | 3.5, Notes | Discrete Fourier Transform; Shift Operator and Circulant Matrices |
| MATLAB Assignment # 3 due 11/7 | |||
| 11/7 | 18 | 3.5, Notes | Diagonalization of Circulant Matrices; Fast Fourier Transform |
| 11/9 | 19 | 5.6 | Cayley-Hamilton Theorem; Canonical forms for matrices |
| 11/14 | 20 | 5.6; App. B | Jordan Canonical Form--Statement and Examples |
| 11/16 | 21 | App. B | Proof of Jordan Canonical Form; Applications to Differential Equations |
| MATLAB Assignment # 4 due 11/22 | |||
| 11/21 | 22 | 6.1-2 | Quadratic Forms; Positive-definite Matrices |
| 11/22 | 23 | 6.2 | Indefinite Quadratic Forms; Law of Inertia |
| 11/28 | 24 | 6.3 | Singular Value Decomposition |
| 11/30 | 25 | 6.4 | Minimum Principles; Rayleigh Quotient |
| 12/5 | 26 | 7.2-3 | Matrix Norm and Condition Number; Power Method |
| 12/7 | 27 | 7.3 | Hessenberg form and QR algorithm |
| MATLAB Assignment # 5 due 12/12 | |||
| 12/12 | 28 | 7.3 | QR algorithm and Inverse Power Method for eigenvectors |
| 12/19 | 12-3 | Final Exam (closed book) |
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