Linear Algebra
I have taught and coordinated Linear Algebra over the course of four years. The lecture notes have changed drastically over these years, and below you will find the most recent version of the notes. You will also find a few supplementary videos that go with some of the lectures. Any lecture that is marked with an asterisk has supplementary videos.
Lecture Notes
Lecture 2: Matrices and Column Spaces
Lecture 3*: Matrix Multiplication, A=CR Factorization
Lecture 4*: Elimination, Elimination Matrices, Permutation Matrices
Lecture 5: Inverse of a Matrix, Transpose of a Matrix
Lecture 6*: A=LU and PA=LU Factorizations, Symmetric Matrices
Lecture 7: Vector Spaces and Subspaces
Lecture 8: The Nullspace of a matrix, Row-Echelon Form (REF), Reduced Row-Echelon Form (RREF)
Lecture 9*: The Complete Solution to a System Ax=b, Rank and Solvability
Lecture 10: Basis and Dimension of a Vector Space
Lecture 11*: Dimensions of the Four Fundamental Subspaces, Orthogonality of the Four Subspaces
Lecture 12: Projections onto Lines and Subspaces
Lecture 13: Least Squares Approximation
Lecture 14: Orthogonal Matrices, Orthogonal Bases, Gram-Schmidt, A=QR Factorization
Lecture 15*: 3 by 3 Determinants, Properties and Applications of Determinants
Lecture 16*: Linear Transformations
Lecture 17: Linear Transformations (Change of Basis)
Lecture 18: Introduction to Eigenvalues
Lecture 19: Introduction to Linear Algebra in Python
Lecture 20: Diagonalizing a Matrix
Lecture 21*: Symmetric Positive Definite Matrices
Lecture 22: Singular Value Decomposition (SVD): Compressing Images by the SVD
Lecture 23: Singular Value Decomposition (SVD): Connections to the Four Fundamental Subspaces
Supplementary Lecture Videos (only for the lectures with *)
Elimination and Permutation Matrices
The Four Fundamental Subspaces
Orthogonality of the Four Subspaces and the Fundamental Theorem of Linear Algebra
Formulas to Compute Determinants
Cofactor Method to Compute Determinants
Matrix of a Linear Transformation