Course contents
- Intro to linear systems, Matrices
- Echelon form of matrices, Gaussian Elimination
- Linear combinations, Matrix-vector & Matrix multiplication
- Properties of matrix multiplication, Elementary matrices
- Matrix inverses and their computation
- LU decomposition, Solving linear systems using LU
- Mass-spring system, Inner products
- Subspaces of ℝ^n, Column spaces and nullspaces
- Abstract vector spaces, Linear independence
- Basis and dimension, The four fundamental subspaces
- Orthogonal complements, Graphs
- Coordinates, Orthonormal bases
- Linear transformations, Coordinate matrix
- Determinants, Cofactor expansion
- Eigenvectors and Eigenvalues and their computation
- Properties of eigenvectors, Markov matrices
- Diagonalization
- Powers of matrices, Matrix Exponential
- Linear Differential Equations
- Orthogonal projection onto lines and subspaces
- Least squares solutions, Linear Regression
- Gram-Schmidt process and QR decomposition
- Spectral Theorem
- Singular value decomposition
- Low rank approximations, Pseudo-Inverse
- Principal Component Analysis
- Review complex numbers, Complex linear algebra
Course resources
Extensive lecture notes for all lectures and practice problems will be provided in the course. Here are some more learning resources:
Textbooks (not required)
- Philip N. Klein — Coding the Matrix: Linear Algebra through Applications to Computer Science, 1st ed., Newtonian Press
- Feryal Alayont & Steven Schlicker — Linear Algebra and Applications: An Inquiry-Based Approach
- David Cherney, Tom Denton, Rohit Thomas & Andrew Waldron — Linear Algebra
- Stephen Boyd & Lieven Vandenberghe — Introduction to Applied Linear Algebra — Vectors, Matrices, and Least Squares
- Gilbert Strang — Linear Algebra and its Applications, 4th ed., Cengage
You are not required to buy any of these textbooks. Please note the coverage and order of topics for these resources may differ from our course.
Videos
- Essence of Linear Algebra by 3Blue1Brown, on YouTube — highly recommended!
- MIT lectures by Gilbert Strang, MIT OpenCourseWare
- Coding the Matrix videos by Philip Klein, on YouTube