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Book cover
  • Book
  • © 1967

Linear Algebra

Authors:

  1. W. H. Greub

    1. Mathematics Department, University of Toronto, Canada

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Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 97)

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Table of contents (14 chapters)

  1. Front Matter

    Pages II-XIV
    PDF

  2. Prerequisites

    • W. H. Greub
    Pages 1-4

  3. Vector Spaces

    • W. H. Greub
    Pages 5-40

  4. Linear Mappings

    • W. H. Greub
    Pages 41-81

  5. Matrices

    • W. H. Greub
    Pages 82-97

  6. Determinants

    • W. H. Greub
    Pages 98-138

  7. Algebras

    • W. H. Greub
    Pages 139-161

  8. Gradations and homology

    • W. H. Greub
    Pages 162-180

  9. Inner product spaces

    • W. H. Greub
    Pages 181-203

  10. Linear mappings of inner product spaces

    • W. H. Greub
    Pages 204-243

  11. Symmetric bilinear functions

    • W. H. Greub
    Pages 244-278

  12. Chapter X Quadrics

    • W. H. Greub
    Pages 279-307

  13. Unitary spaces

    • W. H. Greub
    Pages 308-337

  14. Polynomial algebra

    • W. H. Greub
    Pages 338-367

  15. Theory of a linear transformation

    • W. H. Greub
    Pages 368-427

  16. Back Matter

    Pages 428-434
    PDF
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About this book

The major change between the second and third edition is the separation of linear and multilinear algebra into two different volumes as well as the incorporation of a great deal of new material. However, the essential character of the book remains the same; in other words, the entire presentation continues to be based on an axiomatic treatment of vector spaces. In this first volume the restriction to finite dimensional vector spaces has been eliminated except for those results which do not hold in the infinite dimensional case. The restriction of the coefficient field to the real and complex numbers has also been removed and except for chapters VII to XI, § 5 of chapter I and § 8, chapter IV we allow any coefficient field of characteristic zero. In fact, many of the theorems are valid for modules over a commutative ring. Finally, a large number of problems of different degree of difficulty has been added. Chapter I deals with the general properties of a vector space. The topology of a real vector space of finite dimension is axiomatically characterized in an additional paragraph.
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Keywords

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Authors and Affiliations

  • Mathematics Department, University of Toronto, Canada

    W. H. Greub

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Bibliographic Information

  • Book Title: Linear Algebra

  • Authors: W. H. Greub

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-3-662-00672-6

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1967

  • eBook ISBN: 978-3-662-00672-6Published: 06 December 2012

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 3

  • Topics: Algebra

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Buy it now

eBook USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

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