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Multilinear Algebra

  • Textbook
  • © 1978

Overview

Authors:
  1. Werner Greub

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

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Part of the book series: Universitext (UTX)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-vii
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  2. Tensor Products

    • Werner Greub
    Pages 1-40

  3. Tensor Products of Vector Spaces with Additional Structure

    • Werner Greub
    Pages 41-59

  4. Tensor Algebra

    • Werner Greub
    Pages 60-83

  5. Skew-Symmetry and Symmetry in the Tensor Algebra

    • Werner Greub
    Pages 84-95

  6. Exterior Algebra

    • Werner Greub
    Pages 96-147

  7. Mixed Exterior Algebra

    • Werner Greub
    Pages 148-173

  8. Applications to Linear Transformations

    • Werner Greub
    Pages 174-192

  9. Skew and Skew-Hermitian Transformations

    • Werner Greub
    Pages 193-208

  10. Symmetric Tensor Algebra

    • Werner Greub
    Pages 209-226

  11. Clifford Algebras

    • Werner Greub
    Pages 227-259

  12. Representations of Clifford Algebras

    • Werner Greub
    Pages 260-290

  13. Back Matter

    Pages 291-296
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Keywords

About this book

This book is a revised version of the first edition and is intended as a Linear Algebra sequel and companion volume to the fourth edition of (Graduate Texts in Mathematics 23). As before, the terminology and basic results of Linear Algebra are frequently used without refer~nce. In particular, the reader should be familiar with Chapters 1-5 and the first part of Chapter 6 of that book, although other sections are occasionally used. In this new version of Multilinear Algebra, Chapters 1-5 remain essen­ tially unchanged from the previous edition. Chapter 6 has been completely rewritten and split into three (Chapters 6, 7, and 8). Some of the proofs have been simplified and a substantial amount of new material has been added. This applies particularly to the study of characteristic coefficients and the Pfaffian. The old Chapter 7 remains as it stood, except that it is now Chapter 9. The old Chapter 8 has been suppressed and the material which it con­ tained (multilinear functions) has been relocated at the end of Chapters 3, 5, and 9. The last two chapters on Clifford algebras and their representations are completely new. In view of the growing importance of Clifford algebras and the relatively few references available, it was felt that these chapters would be useful to both mathematicians and physicists.

Authors and Affiliations

  • Department of Mathematics, University of Toronto, Toronto, Canada

    Werner Greub

Bibliographic Information

  • Book Title: Multilinear Algebra

  • Authors: Werner Greub

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-1-4613-9425-9

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1978

  • Softcover ISBN: 978-0-387-90284-5Published: 24 August 1978

  • eBook ISBN: 978-1-4613-9425-9Published: 06 December 2012

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 2

  • Number of Pages: VIII, 296

  • Additional Information: Originally published as Band 136 of the series: Grund- lehren der mathematischen Wissenschaften

  • Topics: Linear and Multilinear Algebras, Matrix Theory

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