Matrices Methods and Applications [Paperback]

This volume provides a down-to-earth, easily understandable guide to techniques of matrix theory, which are widely used throughout engineering and the physical, life, and social sciences. Fully up-to-date, the book covers a wide range of topics, from basic matrix algebra to such advanced concepts as generalized inverses and Hadamard matrices, and applications to error-correcting codes, control theory, and linear programming. Results are illustrated with many examples drawn from diverse areas of application. Numerous exercises are included to clarify the material presented in the text, which is suitable for undergraduates and graduates alike. Researchers will also benefit from the accessible accounts of advanced matrix techniques.

1. How Matrices Arise
2. Basic Algebra of Matrices
3. Unique Solution to Linear Equations
4. Determinant and Inverse
5. Rank, Non-Unique Solution of Equations, and Applications
6. Eigenvalues and Eigenvectors
7. Quadratic and Hermitian Forms
8. Cononical Forms
9. Matrix Functions
10. Generalized Inverses
11. Polynomials, Stability, and Matrix Equations
12. Polynomial and Rational Matrices
13. Patterned Matrices
14. Miscellaneous Topics

The exposition and organization are excellent. The emphasis on applications is pervasive and well-done. . .the exercises are excellent, and include many special topics which an instructor may utilize to tailor a particular course. . .Barnett's book is invaluable as a resource to quickly become familiar with. . . --Robert Grone,San Diego State University

The book is particularly aimed at the nonmathematician who is interested in how matrices can be used and can be recommended for these groups at all levels as well as an alternative, nonabstract approach for mathematicians. --Mathematical Reviews

The first seven chapters provide a first course on matrices, including applications, and the last seven chapters consistls=