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Linear Algebra

An Introductory Approach

  • Textbook
  • © 1984

Overview

Authors:
  1. Charles W. Curtis

    1. Department of Mathematics, University of Oregon, Eugene, 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-x
    Download chapter PDF

  2. Introduction to Linear Algebra

    • Charles W. Curtis
    Pages 1-15

  3. Vector Spaces and Systems of Linear Equations

    • Charles W. Curtis
    Pages 16-74

  4. Linear Transformations and Matrices

    • Charles W. Curtis
    Pages 75-108

  5. Vector Spaces with an Inner Product

    • Charles W. Curtis
    Pages 109-131

  6. Determinants

    • Charles W. Curtis
    Pages 132-162

  7. Polynomials and Complex Numbers

    • Charles W. Curtis
    Pages 163-183

  8. The Theory of a Single Linear Transformation

    • Charles W. Curtis
    Pages 184-227

  9. Dual Vector Spaces and Multilinear Algebra

    • Charles W. Curtis
    Pages 228-265

  10. Orthogonal and Unitary Transformations

    • Charles W. Curtis
    Pages 266-288

  11. Some Applications of Linear Algebra

    • Charles W. Curtis
    Pages 289-323

  12. Back Matter

    Pages 325-349
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Keywords

About this book

Linear algebra is the branch of mathematics that has grown from a care­ ful study of the problem of solving systems of linear equations. The ideas that developed in this way have become part of the language of much of higher mathematics. They also provide a framework for appli­ cations of linear algebra to many problems in mathematics, the natural sciences, economics, and computer science. This book is the revised fourth edition of a textbook designed for upper division courses in linear algebra. While it does not presuppose an earlier course, many connections between linear algebra and under­ graduate analysis are worked into the discussion, making it best suited for students who have completed the calculus sequence. For many students, this may be the first course in which proofs of the main results are presented on an equal footing with methods for solving numerical problems. The concepts needed to understand the proofs are shown to emerge naturally from attempts to solve concrete problems. This connection is illustrated by worked examples in almost every section. Many numerical exercises are included, which use all the ideas, and develop important techniques for problem-solving. There are also theoretical exercises, which provide opportunities for students to discover interesting things for themselves, and to write mathematical explanations in a convincing way. Answers and hints for many of the problems are given in the back. Not all answers are given, however, to encourage students to learn how to check their work.

Reviews

Fourth Edition

C.W. Curtis

Linear Algebra

An Introductory Approach.

"This book is an important addition to the literature of linear algebra. It would be a pleasure to use it for a one-semester or two-quarter course intended for serious (and talented) students. This book deserves to be as influential with the current generation of mathematics students as was Halmos’ Finite-Dimensional Vector Spaces with this reviewer’s generation, 45 years ago."—MATHEMATICAL REVIEWS

Authors and Affiliations

  • Department of Mathematics, University of Oregon, Eugene, USA

    Charles W. Curtis

About the author



Bibliographic Information

  • Book Title: Linear Algebra

  • Book Subtitle: An Introductory Approach

  • Authors: Charles W. Curtis

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-1136-5

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1984

  • Hardcover ISBN: 978-0-387-90992-9Published: 02 May 1984

  • Softcover ISBN: 978-1-4612-7019-5Published: 17 October 2012

  • eBook ISBN: 978-1-4612-1136-5Published: 06 December 2012

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 4

  • Number of Pages: X, 350

  • Additional Information: Originally published by Allyn & Bacon, New Jersey, 1963, 1968 and 1974

  • Topics: Linear and Multilinear Algebras, Matrix Theory

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