The
Geometry of Linear Equations 
Elimination
with Matrices 
Multiplication
and Inverse Matrices 
Factorization
into A=LU 
Transposes,
Permutations, Spaces R^{n} 
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 GramSchmidt 
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 




