**Graduate Studies in Mathematics**

Volume: 78;
2013;
585 pp;
Hardcover

MSC: Primary 15; 30; 34; 39; 52; 93;

Print ISBN: 978-1-4704-0908-1

Product Code: GSM/78.R

List Price: $91.00

Individual Member Price: $72.80

**Electronic ISBN: 978-1-4704-1443-6
Product Code: GSM/78.R.E**

List Price: $91.00

Individual Member Price: $72.80

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# Linear Algebra in Action: Second Edition

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*Harry Dym*

It is a wonderful book: very accessible and rigorous [at] the same time, containing basic and not-so-basic facts, discussing many (sometimes unexpected) applications … Given that and the wonderful way this book was written and organized, I think it can be used by many readers: engineering students, mathematics students, research mathematicians, and researchers in any other field where linear algebra is applied. I strongly recommend this book to anyone interested in “working” linear algebra.

—MAA Reviews

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 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.

#### Table of Contents

# Table of Contents

## Linear Algebra in Action: Second Edition

- Cover Cover11 free
- Title page i2 free
- Contents v6 free
- Preface to the second edition xv16 free
- Preface xvii18 free
- Vector spaces 122 free
- Gaussian elimination 2142
- Additional applications of Gaussian elimination 4566
- Eigenvalues and eigenvectors 6182
- Determinants 91112
- Calculating Jordan forms 113134
- Normed linear spaces 133154
- Inner product spaces and orthogonality 161182
- Symmetric, Hermitian and normal matrices 191212
- Singular values and related inequalities 213234
- Pseudoinverses 237258
- Triangular factorization and positive definite matrices 251272
- Difference equations and differential equations 291312
- Vector valued functions 315336
- The implicit function theorem 337358
- Extremal problems 359380
- Matrix valued holomorphic functions 387408
- Matrix equations 415436
- Realization theory 435456
- Eigenvalue location problems 467488
- Zero location problems 487508
- Convexity 507528
- Matrices with nonnegative entries 537558
- Appendix A. Some facts from analysis 559580
- Appendix B. More complex variables 565586
- Bibliography 575596
- Notation index 579600
- Subject index 581602
- Back Cover Back Cover1610

#### Readership

Graduate students interested in linear algebra or any subject that uses linear algebra.

#### Reviews

*Linear Algebra in Action* ... occupies a
position on my primary bookshelf - the place where I keep the books I will want
to have handy when I am working on mathematics. ... Whereas most books in
mathematics do not have much personality, Dym's book does: it is enlivened with
quotes (many of them from baseball, some witty, some off the wall, all worthy)
and is written in a manner that seems almost to have been transcribed word for
word from an oral lecture. The voice of the "teacher" is present throughout the
text. ... Dym's book is ... a singular and significant addition to the
literature, with many important topics treated here in one volume. The emphasis
on examples will be appreciated by many. ... It is gratifying to see the
inclusion of *Linear Algebra in Action* in the high quality AMS Graduate
Studies in Mathematics series, as it is an indirect affirmation of a subject
that is both important and vibrant. Dym's book should go far in bringing
serious matrix analysis to the next generation of mathematicians.

-- Doug Farenick, IMAGE, The Bulletin of the International Linear Algebra Society