M,W 2-3:15
Clark 102
T:
| Key Topics | Notes |
|---|---|
| Introduction and Definitions | |
| Span and Linear Independence | |
| Basis and Free Vector Space | |
| Linear Transformations, Matrices, Kernels and Images | |
| Matrices, Dependence on Bases, Equivalence | |
| Quotient Spaces | |
| Isomorphism Theorems, Exactness, and Duality | |
| More properties of Dual Spaces | |
| Introduction to Eigenvectors and Eigenvalues | |
| Eigenbases and Jordan Form | |
| More on Decomposing Spaces into Eigenspaces | |
| Jordan Bases and Examples of Computing Jordan Form | |
| Bilinear Forms | |
| Tensor Products | |
| Matrices for Tensor Products of Maps | |
| Exterior Products I | |
| Exterior Products II | |
| Fun with Wedges | |
| Symmetric Powers and Algebras | |
| Inner Product Spaces | |
| Hilbert Spaces: Topological Parts | |
| Isometries and Miscellaneous Examples | |
| Linear Operators on Hilbert Spaces |