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