| Hardcover ISBN: | 978-1-4704-0908-1 |
| Product Code: | GSM/78.R |
| List Price: | $135.00 |
| MAA Member Price: | $121.50 |
| AMS Member Price: | $108.00 |
| eBook ISBN: | 978-1-4704-1443-6 |
| Product Code: | GSM/78.R.E |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| Hardcover ISBN: | 978-1-4704-0908-1 |
| eBook: ISBN: | 978-1-4704-1443-6 |
| 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: | 978-1-4704-0908-1 |
| Product Code: | GSM/78.R |
| List Price: | $135.00 |
| MAA Member Price: | $121.50 |
| AMS Member Price: | $108.00 |
| eBook ISBN: | 978-1-4704-1443-6 |
| Product Code: | GSM/78.R.E |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| Hardcover ISBN: | 978-1-4704-0908-1 |
| eBook ISBN: | 978-1-4704-1443-6 |
| 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 |
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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 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.
ReadershipGraduate students interested in linear algebra or any subject that uses linear algebra.
-
Table of Contents
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Chapters
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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. Vector-valued functions
-
Chapter 15. The implicit function theorem
-
Chapter 16. Extremal problems
-
Chapter 17. Matrix-valued 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
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Appendix A. Some facts from analysis
-
Appendix B. More complex variables
-
-
Additional Material
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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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RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a coursePermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- 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 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.
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. Vector-valued functions
-
Chapter 15. The implicit function theorem
-
Chapter 16. Extremal problems
-
Chapter 17. Matrix-valued 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
