Matrix Analysis

Roger A. Horn, Charles R. Johnson0521386322, 9780521386326, 0521305861

Linear algebra and matrix theory have long been fundamental tools in mathematical disciplines as well as fertile fields for research. In this book the authors present classical and recent results of matrix analysis that have proved to be important to applied mathematics. Facts about matrices, beyond those found in an elementary linear algebra course, are needed to understand virtually any area of mathematical science, but the necessary material has appeared only sporadically in the literature and in university curricula. As interest in applied mathematics has grown, the need for a text and reference offering a broad selection of topics in matrix theory has become apparent, and this book meets that need. This volume reflects two concurrent views of matrix analysis. First, it encompasses topics in linear algebra that have arisen out of the needs of mathematical analysis. Second, it is an approach to real and complex linear algebraic problems that does not hesitate to use notions from analysis. Both views are reflected in its choice and treatment of topics.

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Table of contents :
Contents……Page 002
Preface……Page 004
Ch00 – Review & Miscellanea……Page 007
Ch01 – Eigenvalues, eigenvectors, & similarity……Page 023
Ch02 – Unitary equivalence & normal matrices……Page 039
Ch03 – Canonical forms……Page 066
Ch04 – Hermitin & symmetric matrices……Page 090
Ch05 – Norms for vectors & matrices……Page 135
Ch06 – Location & perturbation of eigenvalues……Page 178
Ch07 – Positive definite matrices……Page 202
Ch08 – Nonnegative matrices……Page 250
Appendix A – Complex Numbers……Page 272
Appendix B – Convex sets & functions……Page 273
Appendix C – The fundamental theorem of algebra……Page 275
Appendix D – Continuous dependence of the zeroes of a polynomial on its coefficients……Page 276
Appendix E – Weierstrass’s theorem……Page 277
References……Page 278
Notation……Page 280
Index……Page 281