Skip to main content
SpringerLink
Log in

Linear Algebra

  • Textbook
  • © 2015

Overview

Authors:
  1. Jörg Liesen

    1. Institute of Mathematics, Technical University of Berlin, Berlin, Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Volker Mehrmann

    1. Institute of Mathematics, Technical University of Berlin, Berlin, Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Provides a matrix-oriented approach to the theory of linear algebra including all details and proofs
  • Improves intuition for students in their first contact with abstract concepts
  • Analyzes detailed examples from application, contains ‘MATLAB-Minutes’ and special topics from applied linear algebra
  • Includes supplementary material: sn.pub/extras

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 14.99 USD 29.99
50% discount Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 19.99 USD 37.99
47% discount Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (20 chapters)

  1. The Kronecker Product and Linear Matrix Equations

    • Jörg Liesen, Volker Mehrmann
    Pages 303-310

  2. Back Matter

    Pages 311-324
    Download chapter PDF
Back to top

Keywords

About this book

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.

Reviews

“This book begins with applied problems that are examined as the theory is developed. … Liesen and Mehrmann … present computations with matrix groups and rings, elementary matrices, echelon forms, rank, linear systems, determinants, and eigenvalues and eigenvectors before introducing vectors and vector spaces. … Each chapter ends with a set of exercises addressing both computation and theory. … Summing Up: Recommended. Upper-division undergraduates through professionals/practitioners.” (J. R. Burke, Choice, Vol. 53 (12), September, 2016)

“It provides a good introductory undergraduate course at an intermediate level … . From the beginning, the authors motivate the material with interesting examples … . the text includes short ‘MATLAB-Minutes’ which are exercises providing an informal introduction to the use of MATLAB in linear algebra, including hints about how care may be needed when working in finite precision.” (John D. Dixon, zbMATH 1334.15001, 2016)

Authors and Affiliations

  • Institute of Mathematics, Technical University of Berlin, Berlin, Germany

    Jörg Liesen, Volker Mehrmann

About the authors

Jörg Liesen's research interests are in Numerical Linear Algebra, Matrix Theory and Constructive Approximation, with a particular focus on the convergence and stability analysis of iterative methods. He is also interested in the history of Mathematics, and in particular of Linear Algebra. He is the recipient of several prizes and awards for his mathematical work, including the Householder Award, the Emmy Noether Fellowship and the Heisenberg Professorship of the DFG. He likes to teach and pursue Mathematics as a lively subject, connecting theory with an ever increasing variety of fascinating applications. 


Volker Mehrmann's research interests are in Numerical Mathematics, Control Theory, Matrix Theory as well as Scientific Computing. In recent years he has focused on the development and analysis of numerical methods for nonlinear eigenvalue problems and differential-algebraic systems with applications in many fields such as mechanical systems, electronic circuit simulation and acoustic field computations. He is co-editor-in-chief of the journal Linear Algebra and its Applications and editor of many other journals in Linear Algebra and Numerical Analysis. He believes that Mathematics has become a central prerequisite for the societal development of the 21st century and that mathematical methods play the key role in the modeling, simulation, control and optimization of all are as of technological development.

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation