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Linear Algebra

An Introduction to Abstract Mathematics

  • Textbook
  • © 1993

Overview

Authors:
  1. Robert J. Valenza

    1. Department of Mathematics, Claremont McKenna College, Claremont, USA

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Part of the book series: Undergraduate Texts in Mathematics (UTM)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xviii
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  2. Sets and Functions

    • Robert J. Valenza
    Pages 1-17

  3. Groups and Group Homomorphisms

    • Robert J. Valenza
    Pages 18-36

  4. Vector Spaces and Linear Transformations

    • Robert J. Valenza
    Pages 37-58

  5. Dimension

    • Robert J. Valenza
    Pages 59-77

  6. Matrices

    • Robert J. Valenza
    Pages 78-99

  7. Representation of Linear Transformations

    • Robert J. Valenza
    Pages 100-130

  8. Inner Product Spaces

    • Robert J. Valenza
    Pages 131-150

  9. Determinants

    • Robert J. Valenza
    Pages 151-168

  10. Eigenvalues and Eigenvectors

    • Robert J. Valenza
    Pages 169-186

  11. Triangulation and Decomposition of Endomorphisms

    • Robert J. Valenza
    Pages 187-213

  12. Back Matter

    Pages 214-237
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Keywords

About this book

Based on lectures given at Claremont McKenna College, this text constitutes a substantial, abstract introduction to linear algebra. The presentation emphasizes the structural elements over the computational - for example by connecting matrices to linear transformations from the outset - and prepares the student for further study of abstract mathematics. Uniquely among algebra texts at this level, it introduces group theory early in the discussion, as an example of the rigorous development of informal axiomatic systems.

Authors and Affiliations

  • Department of Mathematics, Claremont McKenna College, Claremont, USA

    Robert J. Valenza

Bibliographic Information

  • Book Title: Linear Algebra

  • Book Subtitle: An Introduction to Abstract Mathematics

  • Authors: Robert J. Valenza

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-0901-0

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1993

  • Hardcover ISBN: 978-0-387-94099-1Published: 26 August 1993

  • Softcover ISBN: 978-1-4612-6940-3Published: 06 October 2012

  • eBook ISBN: 978-1-4612-0901-0Published: 06 December 2012

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 1

  • Number of Pages: XVIII, 237

  • Topics: Algebra, Linear and Multilinear Algebras, Matrix Theory

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