Hardcover ISBN:  9780883853511 
Product Code:  DOL/44 
List Price:  $65.00 
MAA Member Price:  $48.75 
AMS Member Price:  $48.75 
eBook ISBN:  9780883859674 
Product Code:  DOL/44.E 
List Price:  $60.00 
MAA Member Price:  $45.00 
AMS Member Price:  $45.00 
Hardcover ISBN:  9780883853511 
eBook: ISBN:  9780883859674 
Product Code:  DOL/44.B 
List Price:  $125.00 $95.00 
MAA Member Price:  $93.75 $71.25 
AMS Member Price:  $93.75 $71.25 
Hardcover ISBN:  9780883853511 
Product Code:  DOL/44 
List Price:  $65.00 
MAA Member Price:  $48.75 
AMS Member Price:  $48.75 
eBook ISBN:  9780883859674 
Product Code:  DOL/44.E 
List Price:  $60.00 
MAA Member Price:  $45.00 
AMS Member Price:  $45.00 
Hardcover ISBN:  9780883853511 
eBook ISBN:  9780883859674 
Product Code:  DOL/44.B 
List Price:  $125.00 $95.00 
MAA Member Price:  $93.75 $71.25 
AMS Member Price:  $93.75 $71.25 

Book DetailsDolciani Mathematical ExpositionsVolume: 44; 2011; 251 pp
Linear algebra occupies a central place in modern mathematics. This book provides a rigorous and thorough development of linear algebra at an advanced level, and is directed at graduate students and professional mathematicians. It approaches linear algebra from an algebraic point of view, but its selection of topics is governed not only for their importance in linear algebra itself, but also for their applications throughout mathematics. Students in algebra, analysis, and topology will find much of interest and use to them, and the careful treatment and breadth of subject matter will make this book a valuable reference for mathematicians throughout their professional lives.
Topics treated in this book include: vector spaces and linear transformations; dimension counting and applications; representation of linear transformations by matrices; duality; determinants and their uses; rational and especially Jordan canonical form; bilinear forms; inner product spaces; normal linear transformations and the spectral theorem; and an introduction to matrix groups as Lie groups.
The book treats vector spaces in full generality, though it concentrates on the finite dimensional case. Also, it treats vector spaces over arbitrary fields, specializing to algebraically closed fields or to the fields of real and complex numbers as necessary.

Table of Contents

Chapters

Chapter 1. Vector spaces and linear transformations

Chapter 2. Coordinates

Chapter 3. Determinants

Chapter 4. The structure of a linear transformation I

Chapter 5. The structure of a linear transformation II

Chapter 6. Bilinear, sesquilinear, and quadratic forms

Chapter 7. Real and complex inner product spaces

Chapter 8. Matrix groups as Lie groups

Appendix A. Polynomials

Appendix B. Modules over principal ideal domains


Additional Material

Reviews

... this book is excellent, Weintraub keeps the math flowing, appropriately directional and justified, and it is a rare occasion when he passes on including the detailed proof. There are some times when a part of the proof is not included, but it is rare and generally inconsequential. If you have any current or potential need for understanding the theory of linear algebra, this is a book that you need to have on your easy access shelf.
Charles Ashbacher, Journal of Recreational Mathematics 
... This book can be warmly recommended to any student of pure mathematics requiring a precise and concise treatment of all the important and "wellknown" results of linear algebra. The student will be grateful for the direct route that it follows and for the occasional explanations of the "right" way to understand the material.
Rabe von Randow, Zentrallblatt


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 Book Details
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Linear algebra occupies a central place in modern mathematics. This book provides a rigorous and thorough development of linear algebra at an advanced level, and is directed at graduate students and professional mathematicians. It approaches linear algebra from an algebraic point of view, but its selection of topics is governed not only for their importance in linear algebra itself, but also for their applications throughout mathematics. Students in algebra, analysis, and topology will find much of interest and use to them, and the careful treatment and breadth of subject matter will make this book a valuable reference for mathematicians throughout their professional lives.
Topics treated in this book include: vector spaces and linear transformations; dimension counting and applications; representation of linear transformations by matrices; duality; determinants and their uses; rational and especially Jordan canonical form; bilinear forms; inner product spaces; normal linear transformations and the spectral theorem; and an introduction to matrix groups as Lie groups.
The book treats vector spaces in full generality, though it concentrates on the finite dimensional case. Also, it treats vector spaces over arbitrary fields, specializing to algebraically closed fields or to the fields of real and complex numbers as necessary.

Chapters

Chapter 1. Vector spaces and linear transformations

Chapter 2. Coordinates

Chapter 3. Determinants

Chapter 4. The structure of a linear transformation I

Chapter 5. The structure of a linear transformation II

Chapter 6. Bilinear, sesquilinear, and quadratic forms

Chapter 7. Real and complex inner product spaces

Chapter 8. Matrix groups as Lie groups

Appendix A. Polynomials

Appendix B. Modules over principal ideal domains

... this book is excellent, Weintraub keeps the math flowing, appropriately directional and justified, and it is a rare occasion when he passes on including the detailed proof. There are some times when a part of the proof is not included, but it is rare and generally inconsequential. If you have any current or potential need for understanding the theory of linear algebra, this is a book that you need to have on your easy access shelf.
Charles Ashbacher, Journal of Recreational Mathematics 
... This book can be warmly recommended to any student of pure mathematics requiring a precise and concise treatment of all the important and "wellknown" results of linear algebra. The student will be grateful for the direct route that it follows and for the occasional explanations of the "right" way to understand the material.
Rabe von Randow, Zentrallblatt