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Matrix Analysis

Table of Contents

1. Eigenvalues, eigenvectors, and similarity
2. Unitary similarity and unitary equivalence
3. Canonical forms for similarity, and triangular factorizations
4. Hermitian matrices, symmetric matrices, and congruences
5. Norms for vectors and matrices
6. Location and perturbation of eigenvalues
7. Positive definite and semi-definite matrices
8. Positive and nonnegative matrices
Appendix A. Complex numbers
Appendix B. Convex sets and functions
Appendix C. The fundamental theorem of algebra
Appendix D. Continuous dependence of the zeroes of a polynomial on its coefficients
Appendix E. Continuity, compactness, and Weierstrass's theorem
Appendix F. Canonical pairs.

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