Advertisement

Linear Algebra

  • Jörg Liesen
  • Volker Mehrmann

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

Table of contents

  1. Front Matter
    Pages i-xi
  2. Jörg Liesen, Volker Mehrmann
    Pages 1-7
  3. Jörg Liesen, Volker Mehrmann
    Pages 9-21
  4. Jörg Liesen, Volker Mehrmann
    Pages 23-35
  5. Jörg Liesen, Volker Mehrmann
    Pages 37-53
  6. Jörg Liesen, Volker Mehrmann
    Pages 55-71
  7. Jörg Liesen, Volker Mehrmann
    Pages 73-79
  8. Jörg Liesen, Volker Mehrmann
    Pages 81-99
  9. Jörg Liesen, Volker Mehrmann
    Pages 101-113
  10. Jörg Liesen, Volker Mehrmann
    Pages 115-133
  11. Jörg Liesen, Volker Mehrmann
    Pages 135-154
  12. Jörg Liesen, Volker Mehrmann
    Pages 155-166
  13. Jörg Liesen, Volker Mehrmann
    Pages 167-186
  14. Jörg Liesen, Volker Mehrmann
    Pages 187-197
  15. Jörg Liesen, Volker Mehrmann
    Pages 199-212
  16. Jörg Liesen, Volker Mehrmann
    Pages 213-226
  17. Jörg Liesen, Volker Mehrmann
    Pages 227-251
  18. Jörg Liesen, Volker Mehrmann
    Pages 253-269
  19. Jörg Liesen, Volker Mehrmann
    Pages 271-293
  20. Jörg Liesen, Volker Mehrmann
    Pages 295-302
  21. Jörg Liesen, Volker Mehrmann
    Pages 303-310
  22. Back Matter
    Pages 311-324

About this book

Introduction

This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations.

The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exercises.

Keywords

Linear Algebra Matrices Echelon Form Gaussian Elimination Eigenvalues Linear Maps Vector Spaces Polynomials Fundamental Theorem of Algebra Jordan Canonical Form Matrix Functions Singular Value Decomposition Kronecker Product

Authors and affiliations

  • Jörg Liesen
    • 1
  • Volker Mehrmann
    • 2
  1. 1.Institute of MathematicsTechnical University of BerlinBerlinGermany
  2. 2.Institute of MathematicsTechnical University of BerlinBerlinGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-24346-7
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-24344-3
  • Online ISBN 978-3-319-24346-7
  • Series Print ISSN 1615-2085
  • Series Online ISSN 2197-4144
  • Buy this book on publisher's site