| 1 |
The geometry of linear equations |
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| 2 |
Elimination with matrices |
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| 3 |
Matrix operations and inverses |
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| 4 |
LU and LDU factorization |
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| 5 |
Transposes and permutations |
Problem set 1 due |
| 6 |
Vector spaces and subspaces |
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| 7 |
The nullspace: Solving Ax = 0 |
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| 8 |
Rectangular PA = LU and Ax = b |
Problem set 2 due |
| 9 |
Row reduced echelon form |
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| 10 |
Basis and dimension |
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| 11 |
The four fundamental subspaces |
Problem set 3 due |
| 12 |
Exam 1: Chapters 1 to 3.4 |
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| 13 |
Graphs and networks |
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| 14 |
Orthogonality |
Problem set 4 due |
| 15 |
Projections and subspaces |
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| 16 |
Least squares approximations |
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| 17 |
Gram-Schmidt and A = QR |
Problem set 5 due |
| 18 |
Properties of determinants |
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| 19 |
Formulas for determinants |
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| 20 |
Applications of determinants |
Problem set 6 due |
| 21 |
Eigenvalues and eigenvectors |
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| 22 |
Diagonalization |
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| 23 |
Markov matrices |
Problem set 7 due |
| 24 |
Review for exam 2 |
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| 25 |
Exam 2: Chapters 1-5, 6.1-6.2, 8.2 |
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| 26 |
Differential equations |
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| 27 |
Symmetric matrices |
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| 28 |
Positive definite matrices |
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| 29 |
Matrices in engineering |
Problem set 8 due |
| 30 |
Similar matrices |
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| 31 |
Singular value decomposition |
Problem set 9 due |
| 32 |
Fourier series, FFT, complex matrices |
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| 33 |
Linear transformations |
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| 34 |
Choice of basis |
Problem set 10 due |
| 35 |
Linear programming |
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| 36 |
Course review |
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| 37 |
Exam 3: Chapters 1-8 (8.1, 2, 3, 5) |
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| 38 |
Numerical linear algebra |
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| 39 |
Computational science |
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| 40 |
Final exam |
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