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Linear Algebra

  • Textbook
  • © 1975

Overview

Authors:
  1. Werner Greub

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

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Part of the book series: Graduate Texts in Mathematics (GTM, volume 23)

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Table of contents (14 chapters)

  1. Front Matter

    Pages I-XVII
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  2. Prerequisites

    • Werner Greub
    Pages 1-4

  3. Vector Spaces

    • Werner Greub
    Pages 5-40

  4. Linear Mappings

    • Werner Greub
    Pages 41-82

  5. Matrices

    • Werner Greub
    Pages 83-98

  6. Determinants

    • Werner Greub
    Pages 99-143

  7. Algebras

    • Werner Greub
    Pages 144-166

  8. Gradations and homology

    • Werner Greub
    Pages 167-185

  9. Inner product spaces

    • Werner Greub
    Pages 186-215

  10. Linear mappings of inner product spaces

    • Werner Greub
    Pages 216-260

  11. Symmetric bilinear functions

    • Werner Greub
    Pages 261-295

  12. Quadrics

    • Werner Greub
    Pages 296-324

  13. Unitary spaces

    • Werner Greub
    Pages 325-350

  14. Polynomial Algebras

    • Werner Greub
    Pages 351-382

  15. Theory of a linear transformation

    • Werner Greub
    Pages 383-444

  16. Back Matter

    Pages 445-451
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Keywords

About this book

This textbook gives a detailed and comprehensive presentation of linear algebra based on an axiomatic treatment of linear spaces. For this fourth edition some new material has been added to the text, for instance, the intrinsic treatment of the classical adjoint of a linear transformation in Chapter IV, as well as the discussion of quaternions and the classifica­ tion of associative division algebras in Chapter VII. Chapters XII and XIII have been substantially rewritten for the sake of clarity, but the contents remain basically the same as before. Finally, a number of problems covering new topics-e.g. complex structures, Caylay numbers and symplectic spaces - have been added. I should like to thank Mr. M. L. Johnson who made many useful suggestions for the problems in the third edition. I am also grateful to my colleague S. Halperin who assisted in the revision of Chapters XII and XIII and to Mr. F. Gomez who helped to prepare the subject index. Finally, I have to express my deep gratitude to my colleague J. R. Van­ stone who worked closely with me in the preparation of all the revisions and additions and who generously helped with the proof reading.

Authors and Affiliations

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

    Werner Greub

Bibliographic Information

  • Book Title: Linear Algebra

  • Authors: Werner Greub

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4684-9446-4

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1975

  • Hardcover ISBN: 978-0-387-90110-7Published: 30 June 1975

  • Softcover ISBN: 978-1-4684-9448-8Published: 04 July 2012

  • eBook ISBN: 978-1-4684-9446-4Published: 06 December 2012

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 4

  • Number of Pages: XVIII, 452

  • Additional Information: Originally published as volume 97 of the series: Grundlehren der mathematischen Wissenschaften

  • Topics: Linear and Multilinear Algebras, Matrix Theory

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