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A Guide to Advanced Linear Algebra (Dolciani Mathematical Expositions) by Wei…

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Specificaties

Objectstaat
Heel goed: Een boek dat er niet als nieuw uitziet en is gelezen, maar zich in uitstekende staat ...
ISBN
9780883853511
EAN
9780883853511
Subject Area
Mathematics
Publication Name
Guide to Advanced Linear Algebra
Item Length
9.7 in
Publisher
American Mathematical Society
Subject
Algebra / Linear, Algebra / General
Series
Dolciani Mathematical Expositions Ser.
Publication Year
2011
Type
Textbook
Format
Hardcover
Language
English
Item Height
0.8 in
Author
Steven H. Weintraub
Item Width
6.9 in
Item Weight
17.3 Oz
Number of Pages
251 Pages

Over dit product

Product Information

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.

Product Identifiers

Publisher
American Mathematical Society
ISBN-10
0883853515
ISBN-13
9780883853511
eBay Product ID (ePID)
109094860

Product Key Features

Author
Steven H. Weintraub
Publication Name
Guide to Advanced Linear Algebra
Format
Hardcover
Language
English
Subject
Algebra / Linear, Algebra / General
Series
Dolciani Mathematical Expositions Ser.
Publication Year
2011
Type
Textbook
Subject Area
Mathematics
Number of Pages
251 Pages

Dimensions

Item Length
9.7 in
Item Height
0.8 in
Item Width
6.9 in
Item Weight
17.3 Oz

Additional Product Features

LCCN
2011-923993
Series Volume Number
44
LeafCats
378
Lc Classification Number
Qa184.2 .W45 2011
Reviews
Linear algebra has for decades been the course in the undergraduate math major where the transition was made from the formulaic (often called ""plug and chug"") solution of problems to where proofs are the norm. To many, it is really two courses, the first linear algebra without proofs and the second with proofs. Recently, a third course has been added, computational linear algebra where the emphasis is on computer graphics and the generation of images. Nothing impresses potential math majors more than when they are told how many mathematicians work in the film industry. This book fits into the high end of the second course; it is almost exclusively proofs, although the author cannot resist putting in a few pages of computation. It is not suitable for the traditional linear algebra course, not even for the last segment where proofs take over. It is a book for a special topics course in linear algebra for students at the junior/senior level, students preparing for a qualifying exam or for working mathematicians that need an overview of the main results of linear algebra and how they are usually proved. In that niche, 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 ""Linear algebra occupies a central place in pure mathematics. It plays an essential role in such widely differing fields as Galois theory, function spaces and homological algebra. In this context linear algebra is about vector spaces and linear transformations, not about matrices. The natural and perhaps most enlightening approach to the canonical forms for linear transformations on finite-dimensional vector spaces, one of the main goals of this book, is via the basic structure theorems for modules over a principal ideal domain, but the author has not gone that far. The infinite-dimensional case is, however, treated. Thus, the book is for advanced students of pure mathematics and not for those requiring a textbook on numerically applicable linear algebra. It is, moreover, written in a style to which a student of pure mathematics is fully accustomed. Although the book is for advanced students, it begins with the basics, but it does not deal with matrix operations or the solution of systems of linear equations. The chapter headings are: (1) Vector spaces and linear transformations, (2) Coordinates, (3) Determinants, (4) and (5) The structure of a linear transformation I and II, (6) Bilinear, sesquilinear and quadratic forms, (7) Real and complex inner product spaces, (8) Matrix groups as Lie groups, Appendix A: Polynomials. Appendix B: Modules over principal ideal domains. This book can be warmly recommended to any student of pure mathematics requiring a precise and concise treatment of all the important and ""well-known"" 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, ... 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 "well-known" 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
Table of Content
Preface 1. Vector spaces and linear transformations 2. Coordinates 3. Determinants 4. The structure of a linear transformation I 5. The structure of a linear transformation II 6. Bilinear, sesquilinear, and quadratic forms 7. Real and complex inner product spaces 8. Matrix groups as Lie groups A Polynomials B Modules over principal ideal domains Bibliography Index About the Author
Copyright Date
2011
Target Audience
Scholarly & Professional
Dewey Decimal
516.3/55
Dewey Edition
23
Illustrated
Yes

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