Matrices : theory and applications /

Serre (Ecole Normale Superieure de Lyon) offers another volume in this series of mathematics works; it is designed for graduate students or upper-level undergraduates who wish to study matrix theory or need a reference in that subject. The discussion is approached from a strongly algebraic viewpoint and is quite concise and thorough. The content is error-free and clearly written. In the first three chapters some basic results are presented; the latter chapters, which are mostly independent from one another, present the matrix theory behind matrix applications in several fields. For instance, the last three chapters discuss ideas used in numerical linear algebra: matrix factorization, iterative methods for solving linear systems, and approximation of eigen values. The results are not as extensive as one would find in a work specifically devoted to that field, but each chapter contains the basic ideas and one or two deeper results. There are about 170 exercises spread throughout, all theoretical in nature. Extensive bibliography. A useful resource for anyone who uses matrix theory in his or her work. ^BSumming Up: Highly recommended. Upper-division undergraduates through professionals. J. H. Ellison Grove City College