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Week  Topic  Ref 
1  Systems of linear equations examples and applications; row reduction; echelon forms; associated(augmented) matrices 
WILA What is Linear Algebra? SSLE Solving Systems of Linear Equations RREF Reduced RowEchelon Form 
2 
Matrix equations R^{n}; arithmetic of vectors; Ax=b structure of (in)homogeneous solutions 
VO Vector Operations MO Matrix Operations MM Matrix Multiplication 
3 
Matrix operations matrix multiplication; row operations; inverse matrices; span. 
MM Matrix Multiplication MISLE Matrix Inverses and Systems of Linear Equations LC Linear Combinations SS Spanning Sets 
4 
Independence linear independence; column space; solvability; rank 
LI Linear Independence LDS Linear Dependence and Spans CRS Column and Row Spaces 
5  Factorizations, determinants 
DM Determinant of a Matrix PDM Properties of Determinants of Matrices 
6 
Backwards and forwards review; exam; abstract vector spaces 
VS Vector Spaces 
7 
Vector spaces dimension; basis; coordinates 
S Subspaces LISS Linear Independence and Spanning Sets B Bases D Dimension PD Properties of Dimension 
8 
Transformations linear transformations; change of coordinates 
LT Linear Transformations VR Vector Representations MR Matrix Representations CB Change of Basis 
9 
Eigenvectors eigenvalues and eigenvectors; geometry; 
EE Eigenvalues and Eigenvectors PEE Properties of Eigenvalues and Eigenvectors 
10 
Eigenvectors II characteristic polynomial; diagonalization; applications 

11 
Applications markov chains; graph theory; numerics 

12 
Backwards and forwards review; exam; inner products 

13 
Inner products orthogonality; projection; GramSchmidt 
Section O Orthogonality 
14 
Decompositions least squares; QR; SVD 

15 
Wrapping up applications; review 