Linear Algebra in Action (Graduate Studies in Mathematics) 2nd Edition by Harry Dym (PDF)

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 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.

User’s Reviews

Editorial Reviews: Review 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 ReviewsLinear 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

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I think the first few chapters are hard to follow with the style of the exposition, but this is only something bothersome in the first few chapters. From chapter 4 onwards, it feels better. I would recommend having this book in addition to the rest of your linear algebra repertoire.

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