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CAIRO BOOKS's Description
Linear algebra permeates mathematics, perhaps more so than any other single
subject. It plays an essential role in pure and applied mathematics,
statistics, computer science, and many aspects of physics and engineering. This
book conveys in a user-friendly way the basic and advanced techniques of linear
algebra from the point of view of a working analyst. The techniques are
illustrated by a wide sample of applications and examples that are chosen to
highlight the tools of the trade. In short, this is material that the author
wishes he had been taught as a graduate student. Roughly the first third of the
book covers the basic material of a first course in linear algebra. The
remaining chapters are devoted to applications drawn from vector calculus,
numerical analysis, control theory, complex analysis, convexity and functional
analysis. In particular, fixed point theorems, extremal problems, matrix
equations, zero location and eigenvalue location problems, and matrices with
nonnegative entries are discussed. Appendices on useful facts from analysis and
supplementary information from complex function theory are also provided for
the convenience of the reader. The book is suitable as a text or supplementary
reference for a variety of courses on linear algebra and its applications, as
well as for self-study.