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  • © 1953

Lectures in Abstract Algebra

II. Linear Algebra

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Part of the book series: Graduate Texts in Mathematics (GTM, volume 31)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xii
  2. Finite Dimensional Vector Spaces

    • Nathan Jacobson
    Pages 1-30
  3. Linear Transformations

    • Nathan Jacobson
    Pages 31-62
  4. The Theory of a Single Linear Transformation

    • Nathan Jacobson
    Pages 63-114
  5. Sets of Linear Transformations

    • Nathan Jacobson
    Pages 115-135
  6. Bilinear Forms

    • Nathan Jacobson
    Pages 136-171
  7. Euclidean and Unitary Spaces

    • Nathan Jacobson
    Pages 172-198
  8. Products of Vector Spaces

    • Nathan Jacobson
    Pages 199-226
  9. The Ring of Linear Transformations

    • Nathan Jacobson
    Pages 227-237
  10. Infinite Dimensional Vector Spaces

    • Nathan Jacobson
    Pages 238-276
  11. Back Matter

    Pages 277-280

About this book

The present volume is the second in the author's series of three dealing with abstract algebra. For an understanding of this volume a certain familiarity with the basic concepts treated in Volume I: groups, rings, fields, homomorphisms, is presupĀ­posed. However, we have tried to make this account of linear algebra independent of a detailed knowledge of our first volume. References to specific results are given occasionally but some of the fundamental concepts needed have been treated again. In short, it is hoped that this volume can be read with complete understanding by any student who is mathematically sufficiently mature and who has a familiarity with the standard notions of modern algebra. Our point of view in the present volume is basically the abstract conceptual one. However, from time to time we have deviated somewhat from this. Occasionally formal calculational methods yield sharper results. Moreover, the results of linear algebra are not an end in themselves but are essential tools for use in other branches of mathematics and its applications. It is therefore useful to have at hand methods which are constructive and which can be applied in numerical problems. These methods sometimes necessitate a somewhat lengthier discussion but we have felt that their presentation is justified on the grounds indicated. A stuĀ­ dent well versed in abstract algebra will undoubtedly observe short cuts. Some of these have been indicated in footnotes. We have included a large number of exercises in the text.

Keywords

  • Calculation
  • Morphism
  • algebra
  • linear algebra
  • mathematics
  • matrix theory

Authors and Affiliations

  • Department of Mathematics, Yale University, New Haven, USA

    Nathan Jacobson

Bibliographic Information

  • Book Title: Lectures in Abstract Algebra

  • Book Subtitle: II. Linear Algebra

  • Authors: Nathan Jacobson

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4684-7053-6

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: The Editor(s) (if applicable) and The Author(s) 1953

  • Softcover ISBN: 978-1-4684-7055-0Published: 15 January 2013

  • eBook ISBN: 978-1-4684-7053-6Published: 09 March 2013

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: XII, 280

  • Additional Information: Originally published by Van Nostrand Publishing Company 1953

  • Topics: Linear and Multilinear Algebras, Matrix Theory

Buy it now

Buying options

eBook USD 69.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access