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) 
Ranknullity, graph flows 

Lecture 9 (Sep. 24) 
Orthogonality 

Lecture 10 (Sep. 26) 
Projections, Orthogonal bases 

Lecture 11 (Oct. 1) 
Orthogonal bases 

Lecture 12 (Oct. 3) 
GramSchmidt orthogonalization 

Lecture 13 (Oct. 8) 
Compressed sensing 

Lecture 14 (Oct. 15) 
Rotations and scaling 

Lecture 15 (Oct. 17) 
Singularvalue 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 semidefinite matrices, tensor products 

Lecture 27 (Dec. 3) 
Spectral graph analysis 

Lecture 28 (Dec. 5) 
Vector spaces over finite fields 
