Skip to main content
SpringerLink
Log in
Book cover

Multilinear Algebra

  • Book
  • © 1967

Overview

Authors:
  1. W. H. Greub

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

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 136)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
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

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (8 chapters)

  1. Front Matter

    Pages I-XI
    Download chapter PDF

  2. Tensor product

    • W. H. Greub
    Pages 1-41

  3. Tensor product of vector spaces with additional structure

    • W. H. Greub
    Pages 42-60

  4. Tensor algebra

    • W. H. Greub
    Pages 61-82

  5. Skew symmetry and symmetry in the tensor algebra

    • W. H. Greub
    Pages 83-94

  6. Exterior algebra

    • W. H. Greub
    Pages 95-140

  7. Mixed exterior algebra

    • W. H. Greub
    Pages 141-189

  8. Symmetric tensor algebra

    • W. H. Greub
    Pages 190-204

  9. Multilinear functions

    • W. H. Greub
    Pages 205-224

  10. Back Matter

    Pages 225-227
    Download chapter PDF
Back to top

Keywords

About this book

This book is built around the material on multilinear algebra which in chapters VI to IX of the second edition of Linear Algebra was included but exc1uded from the third edition. It is designed to be a sequel and companion volume to the third edition of Linear Algebra. In fact, the terminology and basic results of that book are frequently used without reference. In particular, the reader should be familiar with chapters I to V and the first part of chapter VI although other sections are occasionally used. The essential difference between the present treatment and that of the second edition lies in the full exploitation of universal properties which eliminates the restrietion to vector spaces of finite dimension. Chapter I contains standard material on multilinear mappings and the tensor product of vector spaces. These results are extended in Chapter 11 to vector spaces with additional structure, such as algebras and differ­ ential spaces. The fundamental concept of "tensor product" is used in Chapter 111 to construct the tensor algebra over a given vector space. In the next chapter the link is provided between tensor algebra on the one hand and exterior and symmetrie tensor algebra on the other. Chapter V contains material on exterior algebra which is developed in considerable depth. Exterior algebra techniques are used in the followmg chapter as a powerful tool to obtain matrix-free proofs of many classical theorems on linear transformation.

Authors and Affiliations

  • Mathematics Department, University of Toronto, Toronto, Canada

    W. H. Greub

Bibliographic Information

  • Book Title: Multilinear Algebra

  • Authors: W. H. Greub

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-3-662-00795-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1967

  • eBook ISBN: 978-3-662-00795-2Published: 06 December 2012

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 1

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Algebra

Publish with us

Policies and ethics

Back to top

Search

Navigation