Math 313 — Introduction to linear algebra
This webpage contains my lecture notes for Math 313 at the University of Arizona.
Lecture notes
- Linear systems
- Linear systems and matrices
- Solvability of linear systems
- Parametric solutions of linear systems
- Linear transformations and their matrices
- Linear transformations in geometry
- Linear systems via linear transformations
- Linear independence
- Operations on matrices and linear transformations
- Invertible matrices
- Determinants
- Determinants as areas and volumes
- Vector spaces
- Spans and subspaces
- Null spaces, column spaces, and row spaces
- Bases of vector spaces
- Coordinate systems
- Linear transformations of vector spaces
- Polynomials and linear transformations
- The dimension of a vector space
- Change of basis
- Eigenvectors and eigenvalues
- The characteristic polynomial
- Diagonalization
- Dynamical systems and Markov chains
- Linear recurrences and differential equations
- Complex eigenvalues
- Eigenvectors and linear transformations
- Length and orthogonality of vectors
- Orthogonal sets
- Orthogonal projections
- Orthogonal complements
- The Gram-Schmidt process
- Reflections and projections via matrices
- Least squares problems
- Spectral theorem