| The Geometry of Linear Equations |
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| Elimination with Matrices |
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| Multiplication and Inverse Matrices |
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| Factorization into A = LU |
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| Transposes, Permutations, Spaces R^n |
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| Column Space and Nullspace |
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| Solving Ax = 0: Pivot Variables, Special Solutions |
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| Solving Ax = b: Row Reduced Form R |
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| Independence, Basis, and Dimension |
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| The Four Fundamental Subspaces |
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| Matrix Spaces; Rank 1; Small World Graphs |
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| Graphs, Networks, Incidence Matrices |
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| Quiz 1 Review |
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| Orthogonal Vectors and Subspaces |
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| Projections onto Subspaces |
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| Projection Matrices and Least Squares |
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| Orthogonal Matrices and Gram-Schmidt |
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| Properties of Determinants |
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| Determinant Formulas and Cofactors |
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| Cramer's Rule, Inverse Matrix, and Volume |
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| Eigenvalues and Eigenvectors |
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| Diagonalization and Powers of A |
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| Differential Equations and exp(At) |
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| Markov Matrices; Fourier Series |
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| Quiz 2 Review |
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| Symmetric Matrices and Positive Definiteness |
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| Complex Matrices; Fast Fourier Transform |
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| Positive Definite Matrices and Minima |
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| Similar Matrices and Jordan Form |
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| Singular Value Decomposition |
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| Linear Transformations and Their Matrices |
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| Change of Basis; Image Compression |
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| Quiz 3 Review |
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| Left and Right Inverses; Pseudoinverse |
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| Final Course Review |
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