Schedule

Lecture	Content	Reference
Lecture 1 (Aug. 27)	Solving linear systems of equations Example - Solving differential equations numerically
Lecture 2 (Aug. 29)	Solving linear systems of equations
Lecture 3 (Sep. 3)	Linear equations, Vector spaces
Lecture 4 (Sep. 5)	Vector spaces
Lecture 5 (Sep. 10)	Subspaces of a matrix
Lecture 6 (Sep. 12)	Linear transformations
Lecture 7 (Sep. 17)	Linear independence, bases and dimension
Lecture 8 (Sep. 19)	Rank-nullity, graph flows
Lecture 9 (Sep. 24)	Orthogonality
Lecture 10 (Sep. 26)	Projections, Orthogonal bases
Lecture 11 (Oct. 1)	Orthogonal bases
Lecture 12 (Oct. 3)	Gram-Schmidt orthogonalization
Lecture 13 (Oct. 8)	Compressed sensing
Lecture 14 (Oct. 15)	Rotations and scaling
Lecture 15 (Oct. 17)	Singular-value decomposition
Lecture 16 (Oct. 22)	Stability of linear equations
Lecture 17 (Oct. 24)	Least squares
Lecture 18 (Oct. 26)	Least squares continued
Lecture 19 (Oct. 31)	Introduction to eigenvectors
Lecture 20 (Nov. 5)	How to find eigenvectors
Lecture 21 (Nov. 7)	Page Rank and Markov chains
Lecture 22 (Nov. 12)	Diagonalizable matrices
Lecture 23 (Nov. 14)	Special matrices
Lecture 24 (Nov. 19)	Principal component analysis (PCA)
Lecture 25 (Nov. 21)	Quantum physics
Lecture 26 (Nov. 26)	Positive semi-definite matrices, tensor products
Lecture 27 (Dec. 3)	Spectral graph analysis
Lecture 28 (Dec. 5)	Vector spaces over finite fields