Hardcover ISBN:  9781470409081 
Product Code:  GSM/78.R 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
eBook ISBN:  9781470414436 
Product Code:  GSM/78.R.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9781470409081 
eBook: ISBN:  9781470414436 
Product Code:  GSM/78.R.B 
List Price:  $220.00 $177.50 
MAA Member Price:  $198.00 $159.75 
AMS Member Price:  $176.00 $142.00 
Hardcover ISBN:  9781470409081 
Product Code:  GSM/78.R 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
eBook ISBN:  9781470414436 
Product Code:  GSM/78.R.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9781470409081 
eBook ISBN:  9781470414436 
Product Code:  GSM/78.R.B 
List Price:  $220.00 $177.50 
MAA Member Price:  $198.00 $159.75 
AMS Member Price:  $176.00 $142.00 

Book DetailsGraduate Studies in MathematicsVolume: 78; 2013; 585 ppMSC: Primary 15; 30; 34; 39; 52; 93
Now available in Third Edition: GSM/232
It is a wonderful book: very accessible and rigorous [at] the same time, containing basic and notsobasic 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 userfriendly 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 NevanlinnaPick 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.
ReadershipGraduate students interested in linear algebra or any subject that uses linear algebra.

Table of Contents

Chapters

Chapter 1. Vector spaces

Chapter 2. Gaussian elimination

Chapter 3. Additional applications of Gaussian elimination

Chapter 4. Eigenvalues and eigenvectors

Chapter 5. Determinants

Chapter 6. Calculating Jordan forms

Chapter 7. Normed linear spaces

Chapter 8. Inner product spaces and orthogonality

Chapter 9. Symmetric, Hermitian and normal matrices

Chapter 10. Singular values and related inequalities

Chapter 11. Pseudoinverses

Chapter 12. Triangular factorization and positive definite matrices

Chapter 13. Difference equations and differential equations

Chapter 14. Vectorvalued functions

Chapter 15. The implicit function theorem

Chapter 16. Extremal problems

Chapter 17. Matrixvalued holomorphic functions

Chapter 18. Matrix equations

Chapter 19. Realization theory

Chapter 20. Eigenvalue location problems

Chapter 21. Zero location problems

Chapter 22. Convexity

Chapter 23. Matrices with nonnegative entries

Appendix A. Some facts from analysis

Appendix B. More complex variables


Additional Material

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


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 Book Details
 Table of Contents
 Additional Material
 Reviews
 Requests
Now available in Third Edition: GSM/232
It is a wonderful book: very accessible and rigorous [at] the same time, containing basic and notsobasic 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 userfriendly 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 NevanlinnaPick 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.
Graduate students interested in linear algebra or any subject that uses linear algebra.

Chapters

Chapter 1. Vector spaces

Chapter 2. Gaussian elimination

Chapter 3. Additional applications of Gaussian elimination

Chapter 4. Eigenvalues and eigenvectors

Chapter 5. Determinants

Chapter 6. Calculating Jordan forms

Chapter 7. Normed linear spaces

Chapter 8. Inner product spaces and orthogonality

Chapter 9. Symmetric, Hermitian and normal matrices

Chapter 10. Singular values and related inequalities

Chapter 11. Pseudoinverses

Chapter 12. Triangular factorization and positive definite matrices

Chapter 13. Difference equations and differential equations

Chapter 14. Vectorvalued functions

Chapter 15. The implicit function theorem

Chapter 16. Extremal problems

Chapter 17. Matrixvalued holomorphic functions

Chapter 18. Matrix equations

Chapter 19. Realization theory

Chapter 20. Eigenvalue location problems

Chapter 21. Zero location problems

Chapter 22. Convexity

Chapter 23. Matrices with nonnegative entries

Appendix A. Some facts from analysis

Appendix B. More complex variables

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