Skip to main content
SpringerLink
Log in

Cyclic dimensions, controllability subspaces and Gohberg-Kaashoek numbers

  • Short Communications
  • Published:
Integral Equations and Operator Theory Aims and scope Submit manuscript

Abstract

A theorem of Macaev and Olshevsky on cyclic dimensions of a matrix is placed in a system theoretic context. Two alternative proofs of the theorem, emerging from ideas from system theory, are presented.

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

References

  1. H. den Boer, G.Ph.A. Thijsse, Semi-stability of sums of partial multiplicities under additive perturbations,Integral Equations and Operator Theory 3 (1980), 23–42.

    Google Scholar 

  2. F.R. Gantmacher,The Theory of Matrices, Vol. 1, Chelsea, 1959

  3. I.M. Gel'fand,Lectures on Linear Algebra, Interscience, New York, 1961, republished Dover, New York, 1989.

    Google Scholar 

  4. I. Gohberg, M.A. Kaashoek, Unsolved problems in matrix and operator theory,Integral Equations and Operator Theory 1 (1978), 278–283.

    Google Scholar 

  5. I. Gohberg, M.A. Kaashoek, F. van Schagen, Eigenvalues of completions of submatrices,Linear Multilinear Algebra 25 (1989), 55–70.

    Google Scholar 

  6. I. Gohberg, M.A. Kaashoek, F. van Schagen,Partially Specified Matrices: Similarity, Completions and Applications, Operator Theory: Advances and Applications, Birkhäuser, Basel, to appear.

  7. P. Lancaster, M. Tismenetsky,The Theory of Matrices, Academic Press, Orlando, 1985.

    Google Scholar 

  8. V. Macaev, V. Olshevsky, Cyclic dimensions, kernel multiplicities and Gohberg-Kaashoek numbers,Linear Algebra Appl., to appear.

  9. A. Markus, E. Parilis, The change of the Jordan structure of a matrix under small perturbations,Mat. Issled. 54 (1980), 98–109 (in Russian),English translation: Linear Algebra Appl. 54, (1983) 139–152.

    Google Scholar 

  10. V.R. Olshevsky, Change of Jordan structure ofG-selfadjoint operators and selfadjoint operator-valued functions under small perturbations,Math. USSR Izvestiya 37 (1991), 371–395.

    Google Scholar 

  11. W.H. Rosenbrock,State space and multivariable theory, Nelson, London, 1970.

    Google Scholar 

  12. I. Zaballa, Interlacing and majorization in invariant factor assignment problems,Linear Algebra Appl. 121 (1989), 409–421.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculteit Wiskunde en Informatica, Vrije Universiteit, De Boelelaan 1081a, 1081HV, Amsterdam, The Netherlands

    F. van Schagen

Authors
  1. F. van Schagen
    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

van Schagen, F. Cyclic dimensions, controllability subspaces and Gohberg-Kaashoek numbers. Integr equ oper theory 22, 248–252 (1995). https://doi.org/10.1007/BF01208353

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01208353

AMS Classification numbers

Search

Navigation