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Basic Linear Algebra

  • Textbook
  • © 1998

Overview

Authors:
  1. Thomas S. Blyth

    1. School of Mathematics and Computer Science, University of St Andrews, North Haugh, St Andrews, UK

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  2. Edmund F. Robertson

    1. School of Mathematics and Computer Science, University of St Andrews, North Haugh, St Andrews, UK

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    You can also search for this author in PubMed   Google Scholar

  • Written with an eye to the changing needs of students * Assumes very little prerequisite knowledge - * Sticks to the core topics *
  • Highlights include treating linear equations via Hermite normal forms and a precise description of the connection between linear mappings and matrices
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Undergraduate Mathematics Series (SUMS)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xi
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  2. The Algebra of Matrices

    • Thomas S. Blyth, Edmund F. Robertson
    Pages 1-15

  3. Some Applications of Matrices

    • Thomas S. Blyth, Edmund F. Robertson
    Pages 16-25

  4. Systems of Linear Equations

    • Thomas S. Blyth, Edmund F. Robertson
    Pages 26-56

  5. Invertible Matrices

    • Thomas S. Blyth, Edmund F. Robertson
    Pages 57-66

  6. Vector Spaces

    • Thomas S. Blyth, Edmund F. Robertson
    Pages 67-91

  7. Linear Mappings

    • Thomas S. Blyth, Edmund F. Robertson
    Pages 92-109

  8. The Matrix Connection

    • Thomas S. Blyth, Edmund F. Robertson
    Pages 110-124

  9. Determinants

    • Thomas S. Blyth, Edmund F. Robertson
    Pages 125-147

  10. Eigenvalues and Eigenvectors

    • Thomas S. Blyth, Edmund F. Robertson
    Pages 148-167

  11. The Minimum Polynomial

    • Thomas S. Blyth, Edmund F. Robertson
    Pages 168-174

  12. Solutions to the Exercises

    • Thomas S. Blyth, Edmund F. Robertson
    Pages 175-199

  13. Back Matter

    Pages 200-201
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Keywords

About this book

Basic Linear Algebra is a text for first year students, working from concrete examples towards abstract theorems, via tutorial-type exercises. The book explains the algebra of matrices with applications to analytic geometry, systems of linear equations, difference equations, and complex numbers. Linear equations are treated via Hermite normal forms, which provides a successful and concrete explanation of the notion of linear independence. Another highlight is the connection between linear mappings and matrices, leading to the change of basis theorem which opens the door to the notion of similarity. The authors are well known algebraists with considerable experience of teaching introductory courses on linear algebra to students at St Andrews. This book is based on one previously published by Chapman and Hall, but it has been extensively updated to include further explanatory text and fully worked solutions to the exercises that all 1st year students should be able to answer.

Authors and Affiliations

  • School of Mathematics and Computer Science, University of St Andrews, North Haugh, St Andrews, UK

    Thomas S. Blyth, Edmund F. Robertson

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