Notes for undergraduate Linear Algebra

The notes below follow closely the textbook Introduction to Linear Algebra, Fourth Edition by Gilbert Strang.

Lecture 3: A Brief Introduction to Matrices

Lecture 4: Solving Linear Systems

Lecture 5: Elimination in terms of Matrix Operations

Lecture 6: Inverse Matrices

Lecture 7: LU Factorization

Lecture 8: Transposes and Permutations

Lecture 9: Vector Spaces

Lecture 10: The Nullspace of a Matrix and Solving Ax=0

Lecture 11: Solving Ax=b in general

Lecture 12: Independence, Basis and Dimension

Lecture 13: Dimensions of the Four Subspaces

Lecture 14: Orthogonality of the Four Subspaces

Lecture 15: Projections

Lecture 16: Least Squares Approximations

Lecture 17: Orthogonal Bases, Orthogonal Matrices, and QR Decomposition

Lecture 18: Introduction to Determinants

Lecture 19: Permutations and Cofactors

Lecture 20: Cramer's rule, Inverses, and Volumes

Lecture 21: Introduction to Eigenvectors and Eigenvalues

Lecture 22: Diagonalizing a Matrix

Lecture 23: Symmetric Matrices

Lecture 24: Positive Definite Matrices

Lecture 25: Similar Matrices

Lecture 26: Singular Value Decomposition (SVD)

Lecture 26 Additional Material: SVD Examples

Lecture 27: Linear Transformations, and their Matrix Representation