Course Description
1. Vector Spaces.
2. Basis and dimension.
3. Matrices, row spaces, column spaces and null spaces.
4. Rank and nullity.
5. Inner product spaces.
6. Inner products and orthonormal bases.
7. Gram-Schmidt process.
8. Least square problems and orthogonal matrices.
9. Eigenvalues and eigenvectors.
10. Diagonalization, orthogonal diagonalization.
11. Linear transformations.
12. Kernel and range.
13. Inverse linear transformations.
14. Similarity.
15. Additional topics include quadratic forms, unitary, normal, Hermitian matrices, and canonical forms.
Intended Learning Outcomes
CILO-1: Summarize and explain the properties of abstract vector spaces.
CILO-2: Describe the poperties of inner product spaces, including orthonormal bases and orthogonal matrices.
CILO-3: Compute the eigenvalues and eigenvectors of a matrix.
CILO-4: Compute the diagonaliztion of some special matrices.