MAT-22A: Linear Algebra

Lecture Notes:

Lecture 1: Vectors and Linear Combinations

Lecture 2: Lengths and Dot Product

Lecture 3: System of Equations: Column and Row Picture

Lecture 4: The Idea of Elimination

Lecture 5: REF and Homogeneous Equations

Lecture 6: Non-homogeneous Equations

Lecture 7: Matrix Operations

Lecture 8: Matrix as Linear Combination and as Linear Transformation

Lecture 9: Inverse Matrix

Lecture 10: Inverse Matrix cont.

Lecture 11: LU Factorization

Lecture 12: Vector Spaces and Subspaces

Lecture 13: Column Space, Null Space, Dependence

Lecture 14: Basis and Dimension

Lecture 15: The Four Subspaces

Lecture 16: Orthogonality of the Four Subspaces

Lecture 17: Projection

Lecture 18: Best Fit Line, Orthonormal Basis

Lecture 19: Gram-Schmidt, QR Factorization

Lecture 20: Determinant

Lecture 21: Eigenvalues and Eigenvectors

Lecture 22: Eigenbasis

Lecture 23: Examples

Lecture 24: Diagonalization

Lecture 25: Applications