Eigenvalues & Diagonalization
A 18-module path through eigenvalues & diagonalization, in study order from foundations to the frontier.
Modules
- Invariant Subspaces
- Eigenvalues and Eigenvectors
- Eigenspaces
- Independence of Eigenvectors for Distinct Eigenvalues
- Existence of Eigenvalues over C
- The Characteristic Polynomial
- Geometric vs Algebraic Multiplicity
- Direct Sum of Eigenspaces
- Diagonalizability and Its Criteria
- Simultaneous Diagonalization of Commuting Operators
- Triangularization of Operators
- The Minimal Polynomial
- The Cayley-Hamilton Theorem
- Minimal Polynomial and Diagonalizability
- Generalized Eigenvectors
- Generalized Eigenspace Decomposition
- The Jordan Canonical Form
- The Rational Canonical Form