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Algebras of Linear Transformations

  • Textbook
  • © 2001

Overview

Authors:
  1. Douglas R. Farenick

    1. Department of Mathematics, University of Regina, Regina, Canada

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Part of the book series: Universitext (UTX)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Linear Algebra

    • Douglas R. Farenick
    Pages 1-37

  3. Algebras

    • Douglas R. Farenick
    Pages 39-75

  4. Invariant Subspaces

    • Douglas R. Farenick
    Pages 77-116

  5. Semisimple Algebras

    • Douglas R. Farenick
    Pages 117-149

  6. Operator Algebras

    • Douglas R. Farenick
    Pages 151-191

  7. Tensor Products

    • Douglas R. Farenick
    Pages 193-232

  8. Back Matter

    Pages 233-239
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Keywords

About this book

The aim of this book is twofold: (i) to give an exposition of the basic theory of finite-dimensional algebras at a levelthat isappropriate for senior undergraduate and first-year graduate students, and (ii) to provide the mathematical foundation needed to prepare the reader for the advanced study of anyone of several fields of mathematics. The subject under study is by no means new-indeed it is classical­ yet a book that offers a straightforward and concrete treatment of this theory seems justified for several reasons. First, algebras and linear trans­ formations in one guise or another are standard features of various parts of modern mathematics. These include well-entrenched fields such as repre­ sentation theory, as well as newer ones such as quantum groups. Second, a study ofthe elementary theory offinite-dimensional algebras is particularly useful in motivating and casting light upon more sophisticated topics such as module theory and operator algebras. Indeed, the reader who acquires a good understanding of the basic theory of algebras is wellpositioned to ap­ preciate results in operator algebras, representation theory, and ring theory. In return for their efforts, readers are rewarded by the results themselves, several of which are fundamental theorems of striking elegance.

Authors and Affiliations

  • Department of Mathematics, University of Regina, Regina, Canada

    Douglas R. Farenick

Bibliographic Information

  • Book Title: Algebras of Linear Transformations

  • Authors: Douglas R. Farenick

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-1-4613-0097-7

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 2001

  • Hardcover ISBN: 978-0-387-95062-4Published: 06 October 2000

  • Softcover ISBN: 978-1-4612-6515-3Published: 15 May 2013

  • eBook ISBN: 978-1-4613-0097-7Published: 06 December 2012

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XIV, 239

  • Topics: Linear and Multilinear Algebras, Matrix Theory

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