Advertisement

Canonical Forms and Factorizations

  • Larisa BeilinaEmail author
  • Evgenii Karchevskii
  • Mikhail Karchevskii
Chapter

Abstract

In this chapter we explore in detail the problem of reducing the matrix of an operator to a simple form using special bases in finite-dimensional spaces. The singular value decomposition of an operator is constructed. The Jordan canonical form of the matrix of a finite-dimensional operator is obtained. A special section is devoted to studying matrix pencils. We obtain their canonical forms and describe applications to investigate the structure of solutions of systems of ordinary linear differential equations.

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Larisa Beilina
    • 1
    Email author
  • Evgenii Karchevskii
    • 2
  • Mikhail Karchevskii
    • 3
  1. 1.Department of Mathematical SciencesChalmers University of Technology and University of GothenburgGothenburgSweden
  2. 2.Department of Applied MathematicsKazan Federal UniversityKazan, Tatarstan RepublicRussia
  3. 3.Department of Computational MathematicsKazan Federal UniversityKazan, Tatarstan RepublicRussia

Personalised recommendations