Description
Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This second edition of this acclaimed text presents results of both classic and recent matrix analysis using canonical forms as a unifying theme and demonstrates their importance in a variety of applications. This thoroughly revised and updated second edition is a text for a second course on linear algebra and has more than 1,100 problems and exercises, new sections on the singular value and CS decompositions and the Weyr canonical form, expanded treatments of inverse problems and of block matrices, and much more.
- Comprehensive coverage of core advanced linear algebra topics, using canonical forms as a unifying theme
- More than 1,100 problems and exercises, many with detailed hints, including theme-based problems that develop throughout the text
- 2-by-2 examples illustrate concepts throughout the book
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’ theorem
Appendix F. Canonical pairs.
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