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Matrix Analysis

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Edition:
2nd
ISBN13:

9780521548236

ISBN10:
0521548233
Format:
Paperback
Pub. Date:
10/22/2012
Publisher(s):
Cambridge University Press
List Price: $55.00

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This is the 2nd edition with a publication date of 10/22/2012.
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Summary

Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This new edition of the acclaimed text presents results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications. The authors have thoroughly revised, updated, and expanded on the first edition. The book opens with an extended summary of useful concepts and facts and includes numerous new topics and features, such as: - New sections on the singular value and CS decompositions - New applications of the Jordan canonical form - A new section on the Weyr canonical form - Expanded treatments of inverse problems and of block matrices - A central role for the Von Neumann trace theorem - A new appendix with a modern list of canonical forms for a pair of Hermitian matrices and for a symmetric-skew symmetric pair - Expanded index with more than 3,500 entries for easy reference - More than 1,100 problems and exercises, many with hints, to reinforce understanding and develop auxiliary themes such as finite-dimensional quantum systems, the compound and adjugate matrices, and the Loewner ellipsoid - A new appendix provides a collection of problem-solving hints.

Table of Contents

Eigenvalues, eigenvectors, and similarity
Unitary similarity and unitary equivalence
Canonical forms for similarity, and triangular factorizations
Hermitian matrices, symmetric matrices, and congruences
Norms for vectors and matrices
Location and perturbation of eigenvalues
Positive definite and semi-definite matrices
Positive and nonnegative matrices
Complex numbers
Convex sets and functions
The fundamental theorem of algebra
Continuous dependence of the zeroes of a polynomial on its coefficients
Continuity, compactness, and Weierstrass's theorem
Canonical pairs
Table of Contents provided by Publisher. All Rights Reserved.


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