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 |
---|---|---|---|
9/1 | 1 | 1.4-5 | Review of Matrix Algebra; Gaussian Elimination by Elementary Matrices |
9/8 | 2 | 1.6 | LU and LDU Factorizations; Matrix Inverses |
9/13 | 3 | 2.1-2 | Vector Spaces and Subspaces; Solving Linear Systems |
9/15 | 4 | 2.3 | Linear Independence, Basis, and Dimension;
Column space, null space, uniqueness of rref(A) |
9/20 | 5 | 2.4, 2.6 | Four Fundamental Subspaces; Linear Transformations and Their Matrices |
MATLAB Assignment # 1 due 9/20 | |||
9/22 | 6 | 3.1-2 | Orthogonal Spaces; Inner Products and Projections |
9/27 | 7 | 3.3 | Projections and Least-squares Approximations |
9/29 | 8 | 3.4 | Orthonormal Bases; Gram-Schmidt Process; QR Factorization |
10/4 | 9 | 4.1-2 | Properties of the Determinant Function |
10/6 | 10 | 4.2-3 | Formulas for Determinants; Permutations |
10/11 | 11 | 4.4 | Determinant Formulas for Matrix Inverse; Cramer's Rule |
10/13 | 12 | 5.1-2 | Eigenvalues and Eigenvectors; Diagonalization |
MATLAB Assignment # 2 due 10/18 | |||
10/18 | 13 | 5.3-4 | Difference and Differential Equations |
10/20 | 14 | Midterm Exam on Chapters 1-4 (closed book) | |
10/25 | 15 | 5.4, 5.5 | Matrix Exponentials; Complex vector spaces; Hermitian matrices |
10/27 | 16 | 5.6 | Schur Triangular Form; Unitary Diagonalization of Normal Matrices |
11/1 | 17 | 3.5, Notes | Discrete Fourier Transform; Shift Operator and Circulant Matrices |
11/3 | 18 | 3.5, Notes | Diagonalization of Circulant Matrices; Fast Fourier Transform |
MATLAB Assignment # 3 due 11/8 | |||
11/8 | 19 | 5.6 | Cayley-Hamilton Theorem; Canonical forms for matrices |
11/10 | 20 | 5.6; App. B | Jordan Canonical Form--Statement and Examples |
11/15 | 21 | App. B | Proof of Jordan Canonical Form; Applications to Differential Equations |
11/17 | 22 | 6.1-2 | Quadratic Forms; Positive-definite Matrices |
MATLAB Assignment # 4 due 11/22 | |||
11/22 | 23 | 6.2 | Indefinite Quadratic Forms; Law of Inertia |
NO CLASS November 24 | |||
11/29 | 24 | 6.3 | Singular Value Decomposition |
12/1 | 25 | 6.4 | Minimum Principles; Rayleigh Quotient |
12/6 | 26 | 7.2-3 | Matrix Norm and Condition Number; Power Method |
12/8 | 27 | 7.3 | Hessenberg form and QR algorithm |
MATLAB Assignment # 5 due 12/13 | |||
12/13 | 28 | 7.3 | QR algorithm and Inverse Power Method for eigenvectors |
12/20 | 12-3 | Final Exam (closed book) |
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