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Basic Linear Algebra

  • Textbook
  • © 2002

Overview

Authors:
  1. T. S. Blyth

    1. School of Mathematical Sciences, University of St Andrews, North Haugh, St Andrews, Fife, Scotland

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  2. E. F. Robertson

    1. School of Mathematical Sciences, University of St Andrews, North Haugh, St Andrews, Fife, Scotland

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • A comprehensive introduction aimed at first-year students, with detailed explanations and fully-worked examples
  • Features additional exercises and new material on Cramer's rule
  • Includes a new chapter on computer assistance in the form of a tutorial on the use of the "Linear Algebra" package in MAPLE 7
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xi
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  2. The Algebra of Matrices

    • T. S. Blyth, E. F. Robertson
    Pages 1-16

  3. Some Applications of Matrices

    • T. S. Blyth, E. F. Robertson
    Pages 17-26

  4. Systems of Linear Equations

    • T. S. Blyth, E. F. Robertson
    Pages 27-58

  5. Invertible Matrices

    • T. S. Blyth, E. F. Robertson
    Pages 59-68

  6. Vector Spaces

    • T. S. Blyth, E. F. Robertson
    Pages 69-94

  7. Linear Mappings

    • T. S. Blyth, E. F. Robertson
    Pages 95-112

  8. The Matrix Connection

    • T. S. Blyth, E. F. Robertson
    Pages 113-128

  9. Determinants

    • T. S. Blyth, E. F. Robertson
    Pages 129-152

  10. Eigenvalues and Eigenvectors

    • T. S. Blyth, E. F. Robertson
    Pages 153-174

  11. The Minimum Polynomial

    • T. S. Blyth, E. F. Robertson
    Pages 175-182

  12. Computer Assistance

    • T. S. Blyth, E. F. Robertson
    Pages 183-204

  13. Solutions to the Exercises

    • T. S. Blyth, E. F. Robertson
    Pages 205-230

  14. Back Matter

    Pages 231-232
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Keywords

About this book

Basic Linear Algebra is a text for first year students leading from concrete examples to abstract theorems, via tutorial-type exercises. More exercises (of the kind a student may expect in examination papers) are grouped at the end of each section. The book covers the most important basics of any first course on linear algebra, explaining 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 important 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. This new and revised edition features additional exercises and coverage of Cramer's rule (omitted from the first edition). However, it is the new, extra chapter on computer assistance that will be ofparticular interest to readers: this will take the form of a tutorial on the use of the "LinearAlgebra" package in MAPLE 7 and will deal with all the aspects of linear algebra developed within the book.

Reviews

From the reviews:

"It embodies a beautiful, concise and precise treatment of the subject, with succint numerical and algebra worked examples at the right points... an excellent textbook which is also eminently suitable for self-study..." Zentralblatt MATH

"This is the second edition of a text for first-year students which covers the main themes of linear algebra in a succinct and readable way. … The book is well-written, with a very high standard of proof-reading, and there are full answers to all the exercises … . It should be welcomed as an excellent introductory textbook which could be used either for self-study and to complement a course of lectures." (Gerry Leversha, The Mathematical Gazette, Vol. 87 (509), 2003)

Authors and Affiliations

  • School of Mathematical Sciences, University of St Andrews, North Haugh, St Andrews, Fife, Scotland

    T. S. Blyth, E. F. Robertson

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