Slides

1. Linear Equations, Back Substitution and Elementary Operations
   Reduction and Echelon Forms

2. Vectors and Linear Combinations
   Matrix Equations
   Linear Independence

3. Introductory Matrix Operations
   Matrix Multiplication
   Matrix Transforms
   Matrix Inverses

4. Determinants: Definitions
   Calculating Determinants

5. Subspaces and Closure
   Bases and Dimension

6. The Three Matrix Spaces
   Coordinate Systems

7. Vector Spaces
   Linear Transforms

8. Eigenvalues
   Properties of Eigenvalues and Eigenvectors
   Similarity and Diagonalization

9. The Dot Product and Orthogonal Vectors
   Orthogonal Complements and Orthonormal Matrices
   Projections
   Iterative Orthogonalization