Text: Gilbert Strang, Linear Algebra and its Applications,
Fourth Edition (New in 2005)
ISBN 0-03-010567-6, Thomson -- Brooks/Cole, 2006.
The following is based on the Fall 2005 syllabus. Some revision is likely. In particular, an attempt will be made to speed up the treatment of chapters 2 and 3 to allow more of the supplements to the summer version of this course to be used.
| Date | Lecture | Reading | Topics |
|---|---|---|---|
| 9/6 | 1 | 1.4-5 | Review of Matrix Algebra; Gaussian Elimination by Elementary Matrices |
| 9/11 | 2 | 1.6 | LU and LDU Factorizations; Matrix Inverses |
| 9/13 | 3 | 2.1-2 | Vector Spaces and Subspaces; Solving Linear Systems |
| 9/18 | 4 | 2.3-4 | Linear Independence, Basis, and Dimension; Four Fundamental Subspaces |
| 9/20 | 5 | 2.6, 2.Review | Linear Transformations and Their Matrices |
| MATLAB Assignment # 1 due 9/25 | |||
| 9/25 | 6 | 3.1-2 | Orthogonal Spaces; Inner Products and Projections |
| 9/27 | 7 | 3.3 | Projections and Least-squares Approximations |
| 10/2 | 8 | 3.4, 3.Review | Orthonormal Bases; Gram-Schmidt Process; QR Factorization |
| 10/4 | 9 | 4.1-2 | Properties of the Determinant Function |
| 10/9 | 10 | 4.2-3, Notes | Formulas for Determinants; Permutations; the Cauchy-Binet formula |
| 10/11 | 11 | 4.4, 4.Review | Determinant Formulas for Matrix Inverse; Cramer's Rule |
| MATLAB Assignment # 2 due 10/16 | |||
| 10/16 | 12 | 5.1-2, Notes | Eigenvalues and Eigenvectors; Diagonalization |
| 10/18 | 13 | 5.3-4, Notes | Difference and Differential Equations. The Perron-Frobenius theorem |
| 10/23 | 14 | Midterm Exam on Chapters 1-4 (closed book) | |
| 10/25 | 15 | 5.4, 5.5, Notes | Matrix Exponentials; Complex vector spaces; Hermitian matrices |
| 10/30 | 16 | 5.6 | Schur Triangular Form; Unitary Diagonalization of Normal Matrices |
| 11/1 | 17 | 3.5 | Discrete Fourier Transform; Shift Operator and Circulant Matrices |
| MATLAB Assignment # 3 due 11/6 | |||
| 11/6 | 18 | 3.5 | Diagonalization of Circulant Matrices; Fast Fourier Transform |
| 11/8 | 19 | 5.6, Notes | Cayley-Hamilton Theorem; Canonical forms for matrices |
| 11/13 | 20 | 5.6, 5.Review; App. B | Jordan Canonical Form--Statement and Examples |
| 11/15 | 21 | App. B | Proof of Jordan Canonical Form; Applications to Differential Equations |
| 11/20 | 22 | 6.1-2 | Quadratic Forms; Positive-definite Matrices |
| 11/27 | 23 | 6.2 | Indefinite Quadratic Forms; Law of Inertia |
| 11/29 | 24 | 6.3, Notes | Singular Value Decomposition |
| MATLAB Assignment # 4, originally due 11/27, now due 12/4 | |||
| 12/4 | 25 | 6.4 | Minimum Principles; Rayleigh Quotient |
| 12/6 | 26 | 7.2-3 | Matrix Norm and Condition Number; Power Method |
| MATLAB Assignment # 5 due 12/11 | |||
| 12/11 | 27 | 7.3 | Hessenberg form and QR algorithm |
| 12/13 | 28 | 7.3 | QR algorithm and Inverse Power Method for eigenvectors |
| 12/22 | 8-11 | Final Exam (closed book) |
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