Skip to main content
SpringerLink
Log in

The portion of matrices with real spectrum in the Lie algebra of the real symplectic group

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

The portion of matrices with real spectrum in a given matrix Lie algebra is the ratio of the volume of the set of matrices with real spectrum in a ball centered at the zero of the algebra to the volume of the entire ball. In this article we calculate the portion of matrices with real spectrum in the Lie algebra of the real symplectic group.

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. Godunov S. K., Modern Aspects of Linear Algebra [in Russian], Nauchnaya Kniga, Novosibirsk (1997).

    MATH  Google Scholar 

  2. Madan Lal Mehta, Random Matrices, Elsevier Acad. Press, Amsterdam (2004).

    MATH  Google Scholar 

  3. Girko V. L., “Random matrices,” in: Handbook of Algebra, ed. Hazewinkel. Vol. 1, North-Holland, Amsterdam, 1996, pp. 27–78.

    Google Scholar 

  4. Edelman A. and Raj Rao N., “Random matrix theory,” Acta Numer., 14, No. 1, 233–297 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  5. Edelman A., “The probability that a random real Gaussian matrix has k real eigenvalues, related distributions, and the circular law,” J. Multivariate Anal., 60, No. 2, 203–232 (1997).

    Article  MATH  MathSciNet  Google Scholar 

  6. Krivonogov A. S., “A portion of matrices with real spectrum in a real symplectic Lie algebra,” Algebra and Logic, 50, No. 4, 375–379 (2011).

    Article  MATH  MathSciNet  Google Scholar 

  7. Zelikin M. I., Homogeneous Spaces and the Riccati Equation in the Calculus of Variations [in Russian], Faktorial, Moscow (1998).

    MATH  Google Scholar 

  8. Humphreys J. E., Introduction to Lie Algebras and Representation Theory, Springer-Verlag, New York, Heidelberg, and Berlin (1980).

    MATH  Google Scholar 

  9. Kobayashi Sh. and Nomizu K., Foundations of Differential Geometry. Vol. 2, Interscience Publishers, New York and London (1969).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Novosibirsk State University, Novosibirsk, Russia

    A. S. Krivonogov

  2. Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk, Russia

    V. A. Churkin

Authors
  1. A. S. Krivonogov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. A. Churkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. S. Krivonogov.

Additional information

Original Russian Text Copyright © 2014 Krivonogov A.S. and Churkin V.A.

The authors were supported by the Russian Science Foundation (Grant RNF 14-21-00065).

__________

Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 55, No. 6, pp. 1297–1314, November–December, 2014.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Krivonogov, A.S., Churkin, V.A. The portion of matrices with real spectrum in the Lie algebra of the real symplectic group. Sib Math J 55, 1056–1072 (2014). https://doi.org/10.1134/S0037446614060081

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0037446614060081

Keywords

Search

Navigation