Matrix Analysis

Roger A. Horn is a Research Professor in the Department of Mathematics at the University of Utah. He is co-author of Topics in Matrix Analysis (Cambridge University Press, 1994). Charles R. Johnson is a Professor in the Department of Mathematics at the College of William and Mary. He is co-author of Topics in Matrix Analysis (Cambridge University Press, 1994).

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' theorem; Appendix F. Canonical pairs.