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 many of us wish we 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.
In this new edition, most of the chapters in the first edition have been
revised, some extensively.The revisions include changes in a number of
proofs, either to simplify the argument, to make the logic clearer or,
on occasion, to sharpen the result. New introductory sections on linear
programming, extreme points for polyhedra and a Nevanlinna-Pick
interpolation problem have been added, as have some very short
introductory sections on the mathematics behind Google, Drazin inverses,
band inverses and applications of SVD together with a number of new
exercises.
