Matrix theory. Basic results and techniques. (English) Zbl 0948.15001

Zhang, Fuzhen

Universitext. New York, NY: Springer. xiii, 277 p. (1999).

This book is not an introductory text on linear algebra. It is a comprehensive textbook on matrices for readers with an elementary linear algebra background. Matrices are widely used in a great variety of different areas, and this book is aimed at students and applied mathematicians requiring a sound textbook approach to matrix theory.
The chapter headings are: 1. Elementary linear algebra review, 2. Partitioned matrices, 3. Matrix polynomials and canonical forms, 4. Special types of matrices, 5. Unitary matrices and contractions, 6. Positive semidefinite matrices, 7. Hermitian matrices, 8. Normal matrices.
Each chapter contains one or more extensive sections of problems. The book covers a great deal of ground and will be very useful as a source of information both for the student and for the practising mathematician, and as a textbook for a second course in linear algebra.

Reviewer: Rabe von Randow (Bonn)

MSC:

15-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to linear algebra
15A09	Theory of matrix inversion and generalized inverses
15A15	Determinants, permanents, traces, other special matrix functions
15A18	Eigenvalues, singular values, and eigenvectors
15A54	Matrices over function rings in one or more variables
15A21	Canonical forms, reductions, classification
15A60	Norms of matrices, numerical range, applications of functional analysis to matrix theory
15B57	Hermitian, skew-Hermitian, and related matrices
15B51	Stochastic matrices
15A45	Miscellaneous inequalities involving matrices

Keywords:

partitioned matrices; matrix polynomials; unitary matrices; positive semidefinite matrices; normal matrices; hermitian matrices; textbook; canonical forms