Linear Algebra: Invariant Subspaces
نویسنده
چکیده
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. Semisimplicity Versus Potential Diagonalizability 27 10. The Dual Endomorphism 30 10.1. Review of Dual Spaces 30 10.2. The Dual Endomorphism 31 10.3. Jacob’s Proof of the Existence of a Cyclic Decomposition 33 References 34
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