| 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 |
Problem set 1 due |
| 5 |
Transposes and Permutations |
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| 6 |
Vector Spaces and Subspaces |
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| 7 |
The Nullspace: Solving Ax = 0 |
Problem set 2 due |
| 8 |
Rectangular PA = LU and Ax = b |
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| 9 |
Row Reduced Echelon Form |
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| 10 |
Basis and Dimension |
Problem set 3 due |
| 11 |
The Four Fundamental Subspaces |
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| 12 |
Exam 1: Chapters 1 to 3.5 |
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| 13 |
Graphs and Networks |
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| 14 |
Orthogonality |
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| 15 |
Projections and Subspaces |
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| 16 |
Least Squares Approximations |
Problem set 4 due |
| 17 |
Gram-Schmidt and A = QR |
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| 18 |
Properties of Determinants |
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| 19 |
Formulas for Determinants |
Problem set 5 due |
| 20 |
Applications of Determinants |
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| 21 |
Eigenvalues and Eigenvectors |
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| 22 |
Exam Review |
Problem set 6 due |
| 23 |
Exam 2: Chapters 1-5 |
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| 24 |
Diagonalization |
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| 25 |
Markov Matrices |
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| 26 |
Fourier Series and Complex Matrices |
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| 27 |
Differential Equations |
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| 28 |
Symmetric Matrices |
Problem set 7 due |
| 29 |
Positive Definite Matrices |
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| 30 |
Matrices in Engineering |
Problem set 8 due |
| 31 |
Singular Value Decomposition |
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| 32 |
Similar Matrices |
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| 33 |
Linear Transformations |
Problem set 9 due |
| 34 |
Choice of Basis |
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| 35 |
Exam Review |
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| 36 |
Exam 3: Chapters 1-8 (8.1, 2, 3, 5) |
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| 37 |
Fast Fourier Transform |
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| 38 |
Linear Programming |
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| 39 |
Numerical Linear Algebra |
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| 40 |
Final Exams |
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