| 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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