Synopses & Reviews
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.
Synopsis
'Matrix Analysis presents the classical and recent results for matrix analysis that have proved to be important to applied mathematics.'
Synopsis
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 view are reflected in its choice and treatment of topics.
Table of Contents
Preface; Review and miscellanea; 1. Eigenvalues, eigenvectors, and similarity; 2. Unitary equivalence and normal matrices; 3. Canonical forms; 4. Hermitian and symmetric matrices; 5. Norms for vectors and matrices; 6. Location and perturbation of eigenvalues; 7. Positive definite matrices; 8. Non-negative matrices; 9. Appendices; References.