Skip to main content
SpringerLink
Log in

Generalized induced norms

  • Published:
Czechoslovak Mathematical Journal Aims and scope Submit manuscript

Abstract

Let ‖·‖ be a norm on the algebra ℳn of all n × n matrices over ℂ. An interesting problem in matrix theory is that “Are there two norms ‖·‖1 and ‖·‖2 on ℂn such that ‖A‖ = max|‖Ax‖2: ‖x‖1 = 1} for all A ∈ ℳn?” We will investigate this problem and its various aspects and will discuss some conditions under which ‖·‖1 = ‖·‖2.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. R. Belitskii, Yu. I. Lyubich: Matrix Norms and Their Applications. Operator Theory: Advances and Applications, 36. Birkhäuser-Verlag, Basel, 1988.

    MATH  Google Scholar 

  2. R. Bhatia: Matrix Analysis. Graduate Texts in Mathematics, 169. Springer-Verlag, New York, 1997.

    Google Scholar 

  3. R. A. Horn, C. R. Johnson: Matrix Analysis. Cambridge University Press, Cambridge, 1994.

    MATH  Google Scholar 

  4. C.-K. Li, N.-K. Tsing, and F. Zhang: Norm hull of vectors and matrices. Linear Algebra Appl. 257 (1997), 1–27.

    Article  MATH  MathSciNet  Google Scholar 

  5. W. Rudin: Real and Complex Analysis. McGraw-Hill, New York, 1987.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Ferdowsi University, P.O. Box 1159, Mashhad, 91775, Iran

    S. Hejazian, M. Mirzavaziri & M. S. Moslehian

Authors
  1. S. Hejazian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Mirzavaziri
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. S. Moslehian
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hejazian, S., Mirzavaziri, M. & Moslehian, M.S. Generalized induced norms. Czech Math J 57, 127–133 (2007). https://doi.org/10.1007/s10587-007-0049-5

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10587-007-0049-5

Keywords

Search

Navigation