Introduction 1 1. Invariant Subspaces 3 2. Eigenvectors, Eigenvalues and Eigenspaces 11 3. Cyclic Spaces 14 4. Prime and Primary Vectors 15 5. The Cyclic Decomposition Theorem 20 6. Rational and Jordan Canonical Forms 22 7. Similarity 23 8. The Cayley-Hamilton Polynomial (Or: Up With Determinants?) 24 9. Extending The Ground Field 25 9.1. Some Invariances Under Base Extension 25 9.2. Semisimpli...