| Lecture1 |
The Geometry of Linear Equations
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| Lecture2 |
Elimination with Matrices
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| Lecture3 |
Multiplication and Inverse Matrices
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| Lecture4 |
Factorization into A = LU
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| Lecture5 |
Transposes, Permutations, Spaces Rn
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| Lecture6 |
Column Space and Nullspace
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| Lecture7 |
Solving Ax = 0: Pivot Variables, Special Solutions
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| Lecture8 |
Solving Ax = b : Row Reduced Form R
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| Lecture9 |
Independence, Basis, and Dimension
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| Lecture10 |
The Four Fundamental Subspaces
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| Lecture11 |
Matrix Spaces; Rank 1; Small World Graphs
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| Lecture12 |
Graphs, Networks, Incidence Matrices
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| Lecture13 |
Quiz 1 Review
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| Lecture14 |
Orthogonal Vectors and Subspaces
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| Lecture15 |
Projections onto Subspaces
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| Lecture16 |
Projection Matrices and Least Squares
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| Lecture17 |
Orthogonal Matrices and Gram-Schmidt
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| Lecture18 |
Properties of Determinants
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| Lecture19 |
Determinant Formulas and Cofactors
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| Lecture20 |
Cramer's Rule, Inverse Matrix, and Volume
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| Lecture21 |
Eigenvalues and Eigenvectors
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| Lecture22 |
Diagonalization and Powers of A
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| Lecture23 |
Differential Equations and exp(At)
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| Lecture24 |
Markov Matrices; Fourier Series
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| Lecture24.5 |
Quiz 2 Review
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| Lecture25 |
Symmetric Matrices and Positive Definiteness
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| Lecture26 |
Complex Matrices; Fast Fourier Transform
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| Lecture27 |
Positive Definite Matrices and Minima
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| Lecture34 |
Final Course Review
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