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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 graduate students.
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.
