© 2017

Linear Algebra


  • Provides the necessary material clearly, self-contained, provides important exercises with detailed solutions

  • Includes a set of exercises at the end of each chapter

  • Detailed solutions to exercises are provided


Part of the Compact Textbooks in Mathematics book series (CTM)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Belkacem Said-Houari
    Pages 1-68
  3. Belkacem Said-Houari
    Pages 69-120
  4. Belkacem Said-Houari
    Pages 121-158
  5. Belkacem Said-Houari
    Pages 159-198
  6. Belkacem Said-Houari
    Pages 199-225
  7. Belkacem Said-Houari
    Pages 227-268
  8. Belkacem Said-Houari
    Pages 269-321
  9. Belkacem Said-Houari
    Pages 323-376
  10. Back Matter
    Pages 377-384

About this book


This self-contained, clearly written textbook on linear algebra is easily accessible for students. It begins with the simple linear equation and generalizes several notions from this equation for the system of linear equations and introduces the main ideas using matrices. It then offers a detailed chapter on determinants and introduces the main ideas with detailed proofs. The third chapter introduces the Euclidean spaces using very simple geometric ideas and discusses various major inequalities and identities. These ideas offer a solid basis for understanding general Hilbert spaces in functional analysis. The following two chapters address general vector spaces, including some rigorous proofs to all the main results, and linear transformation: areas that are ignored or are poorly explained in many textbooks. Chapter 6 introduces the idea of matrices using linear transformation, which is easier to understand than the usual theory of matrices approach. The final two chapters are more advanced, introducing the necessary concepts of eigenvalues and eigenvectors, as well as the theory of symmetric and orthogonal matrices. Each idea presented is followed by examples.  
The book includes a set of exercises at the end of each chapter, which have been carefully chosen to illustrate the main ideas. Some of them were taken (with some modifications) from recently published papers, and appear in a textbook for the first time. Detailed solutions are provided for every exercise, and these refer to the main theorems in the text when necessary, so students can see the tools used in the solution. 


matrix algebra linear algebra eigenvalues orthogonal matrices symmetric matrices

Authors and affiliations

  1. 1.Department of Mathematics, College of SciencesUniversity of SharjahSharjahUnited Arab Emirates

About the authors

Belkacem Said-Houari is Professor at the Mathematics Department, University of Sharjah, Sharjah and author of the book on Differential Equation (ISBN 978-3-319-25734-1) in the same series.

Bibliographic information

  • Book Title Linear Algebra
  • Authors Belkacem Said-Houari
  • Series Title Compact Textbooks in Mathematics
  • Series Abbreviated Title Compact Textbooks in Mathematics
  • DOI
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-319-63792-1
  • eBook ISBN 978-3-319-63793-8
  • Series ISSN 2296-4568
  • Series E-ISSN 2296-455X
  • Edition Number 1
  • Number of Pages XIII, 384
  • Number of Illustrations 0 b/w illustrations, 26 illustrations in colour
  • Topics Linear and Multilinear Algebras, Matrix Theory
  • Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking


“This book can be used as a textbook for a first course in linear algebra for undergraduate students in all disciplines. It can be also used as a booklet for graduate students, allowing to acquire some concepts, examples, and basic results. It is also suitable for those students who are looking for a simple, easy, and clear textbook that summarizes the main ideas of linear algebra.” (Mihail Voicu, zbMATH 1381.15001, 2018)