| Lecture | Date | Topic | Reading |
|---|---|---|---|
| / | Matrix-vector multiplication, column space, rank, matrix-matrix multiplication, outer product matrix |
Strang I.1 - I.2
Lecture 1 notes |
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| / | four subspaces of a matrix, column space, nullspace, rank(AB), rank(A+B)
A singular, nonsingular, Ax = b, existence and uniqueness, A = LU, PA = LU |
Strang I.3-I.4
Lecture 2 notes Lecture 3 notes |
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| / | |||
| / | Orthogonality, orthogonal vectors, orthogonal subspaces, orthogonal matrix, projector
Eigenvalues, eigenvectors, shifts, similarity |
Strang I.5-I.6
Lecture 4 notes Lecture 5 notes |
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| / | Symmetric positive definite matrices, Cholesky factorization, SVD |
Strang I.7-I.8
Lecture 6 notes Lecture 7 notes |
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| / | SVD, fundamental subspaces of A, pseudoinverse, vector and matrix norms |
Strang I.8, Strang I.11, (Strang II.2, Pseudoinverse subsection)
Lecture 8 notes Lecture 9 notes Example (run at https://octave-online.net) | |
| / | |||
| / | QR decomposition, Gram-Schmidt, Householder
Review session Study Guide |
Strang II.2 (pp. 128-131 (QR by Gram-Schmidt and Householder))
Lecture 10 notes (Craig Schroeder) Sample Midterm (shortened) (Solutions ) |
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| / | Least squares, normal equations, least squares by pseudoinverse (minimum norm solution)
Least squares by QR, Tikhonov regulariation of LS, weighted LS, condition number, matrix condition number (Ax =b) |
Strang II.2
Lecture 12 notes Lecture 13 notes |
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| / | |||
| / | Conditioning and stability
floating point |
Lectures 14-15 notes |
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| / | |||
| / | floating point
HOLIDAY |
Lecture 16 notes |
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| - | / | ||
| / | Iterative methods, Jacobi, Gauss-Seidel, convergence rate,
power iteration, inverse iteration, rayleigh quotient iteration QR algorithm, shifted QR, reduction to upper Hessenberg, Arnoldi iteration, eigenvalues from Arnoldi, symmetric matrcies and Lanczos Krylov vectors, Krylov subspace, residual, GMRES |
Strang II.1
Lecture 17 notes Lecture 18 notes |
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line search, steepest descent method, conjugate gradients methods
Review Session Final Study Guide | Lecture19 notes
Shewchuk Sample Final (shortened) (Solutions) |
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| - | TBD | FINAL |