Lectures (2025)

Lecture 1: Gaussian Elimination 

Textbook Sections 1.1-1.4 

Lecture 2: Linear Independence

Textbook Sections 1.5-1.7

Lecture 3: Linear Transformation

Textbook Sections 1.8-1.9

Lecture 3.1: Linear Transformation Theorems

Textbook Sections 1.9

Lecture 4: Matrix Operations and Inverse Matrix

Textbook Sections 2.1-2.3

Lecture 5: LU Factorization

Textbook Section 2.5

Domo: Matrix Calculator https://matrixcalc.org/ 

Lecture 6: Column space & Null space

Textbook Section 2.8

Lecture 6.1: Basis & Coordinate

Textbook Section 2.9

Lecture 6.2: Four fundamental subspaces 

Lecture 7: Determinants

Textbook Sections 3.1-3.3 

Lecture 8: Eigenvalues and Eigenvectors 

Textbook Sections 5.1-5.2 

Lecture 9:  Diagonalization 

Textbook Sections 5.3 

Lecture 10:  Orthogonality 

Textbook Sections 6.1-6.2 

Lecture 10.1:  Orthogonal Projection 

Textbook Sections 6.3 

Lecture 11:  Gram-Schmidt Process  

Textbook Sections 6.4 

Lecture 12:   Least Square Solution 

Textbook Sections 6.5 

Lecture 13:   Symmetric Matrices  Diagonalization & Quadratic Form 

Textbook Sections 7.1 - 7.2