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Vector and Matrix Norms

  • Larisa BeilinaEmail author
  • Evgenii Karchevskii
  • Mikhail Karchevskii
Chapter

Abstract

In this chapter the concept of a norm on the vector space \({\mathbb {C}}^n\) is introduced. We investigate relationships between different norms. We give the definition of a norm on the space of complex rectangular matrices and study its properties in detail, particularly with regard to estimates of eigenvalues and singular values of operators.

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

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