Lecture Notes
Antoine Cerfon
CIMS, NYU
Home
Research
Teaching
Publications
Codes
Notes for undergraduate Linear Algebra
The notes below follow closely the textbook
Introduction to Linear Algebra, Fourth Edition
by Gilbert Strang.
Lecture 1: Vectors and Linear Combinations
Lecture 2: Lengths and the dot product
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