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 |
---|---|---|---|
9/05 | 1 | 1.4-5 | Review of Matrix Algebra; Gaussian Elimination by Elementary Matrices |
9/10 | 2 | 1.6 | LU and LDU Factorizations; Matrix Inverses |
9/12 | 3 | 2.1-2 | Vector Spaces and Subspaces; Solving Linear Systems |
9/17 | 4 | 2.3 | Linear Independence, Basis, and Dimension;
Column space, null space, uniqueness of rref(A) |
9/19 | 5 | 2.4, 2.6 | Four Fundamental Subspaces; Linear Transformations and Their Matrices |
MATLAB Assignment # 1 due 9/24 | |||
9/24 | 6 | 3.1-2 | Orthogonal Spaces; Inner Products and Projections |
9/26 | 7 | 3.3 | Projections and Least-squares Approximations |
10/1 | 8 | 3.4 | Orthonormal Bases; Gram-Schmidt Process; QR Factorization |
10/3 | 9 | 4.1-2 | Properties of the Determinant Function |
10/8 | 10 | 4.2-3 | Formulas for Determinants; Permutations |
10/10 | 11 | 4.4 | Determinant Formulas for Matrix Inverse; Cramer's Rule |
MATLAB Assignment # 2 due 10/15 | |||
10/15 | 12 | 5.1-2 | Eigenvalues and Eigenvectors; Diagonalization |
10/17 | 13 | 5.3-4 | Difference and Differential Equations |
10/22 | 14 | Midterm Exam on Chapters 1-4 (closed book) | |
10/24 | 15 | 5.4, 5.5 | Matrix Exponentials |
NO CLASS Oct. 29 (Hurricane Sandy) | |||
NO CLASS Oct. 31 (Hurricane Sandy) | |||
11/05 | 18 | 5.5 5.6 |
Complex vector spaces; Hermitian matrices Schur Triangular Form; Unitary Diagonalization of Normal Matrices |
11/07 | 19 | 3.5, Notes | Discrete Fourier Transform; Shift Operator and Circulant Matrices Diagonalization of Circulant Matrices; Fast Fourier Transform |
MATLAB Assignment # 3 due 11/12 | |||
11/12 | 20 | 5.6 | Cayley-Hamilton Theorem; Canonical forms for matrices |
11/14 | 21 | 5.6; App. B | Jordan Canonical Form--Statement and Examples |
11/19 | 22 | App. B | Proof of Jordan Canonical Form; Applications to Differential Equations |
NO CLASS November 21 | |||
MATLAB Assignment # 4 due 11/26 | |||
11/26 | 23 | 6.1-2 | Quadratic Forms; Positive-definite Matrices |
11/28 | 24 | 6.2 | Indefinite Quadratic Forms; Law of Inertia |
12/03 | 25 | 6.3 | Singular Value Decomposition |
12/05 | 26 | 6.4 | Minimum Principles; Rayleigh Quotient |
12/10 | 27 | 7.3 | Hessenberg form and QR algorithm |
MATLAB Assignment # 5 due 12/12 | |||
12/12 | 28 | 7.3 7.4 |
QR algorithm for eigenvalues and inverse power method for eigenvectors
Iterative methods for Ax = b |
12/17 | 12-3 | Final Exam (closed book) |
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