Skip to main content
SpringerLink
Log in

Construction of unital matrix polynomials with mutually distinct characteristic roots

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We investigate the construction of unital matrix polynomials with mutually distinct characteristic roots, namely, their similarity and reducibility by the similarity transformation to block-triangular, block-diagonal, and, in particular, to triangular and diagonal forms. We also study the problem of extracting linear factors.

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. O. M. Mel'nik, “Similarity of unital matrix polynomials,”Dokl. Akad. Nauk Ukr. SSR, Ser. A., No. 5, 11–14 (1984).

    Google Scholar 

  2. P. S. Kazimirskii and O. M. Mel'nik, “Solution of the problem of semiscalar equivalence of polynomial matrices with pairwise distinct characteristic roots,”Dokl. Akad. Nauk Ukr. SSR, Ser. A., No. 11, 9–12 (1988).

    Google Scholar 

  3. O. M. Mel'nik, “Similarity of unital matrix polynomials with pairwise distinct characteristic roots,” in:Abstracts of Papers on the Theory of Rings, Algebras, and Modules (International Conference on Algebra, Novosibirsk, August 21–26, 1989), Novosibirsk (1989), p. 86.

  4. P. S. Kazimirskii and O. M. Mel'nik, “Similarity and construction of unitai matrix square trinomials with pairwise distinct characteristic roots,” Rings and Modules, Vol. 3,Zap. Nauchn. Sem. Leningr. Otd. Mat. lnst. Steklov.,175, 63–68 (1989).

    Google Scholar 

  5. O. M. Mel'nik, “On semiscalar equivalence of polynomial matrices,”Abstracts of the 6th Symposium on the Theory of Rings, Algebras, and Modules, Lvov, September 11–13, 1990, p. 83.

  6. P. S. Kazimirskii,Decomposition of Matrix Polynomials into Factors [in Ukrainian], Naukova Dumka, Kiev (1981).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Applied Problems in Mechanics and Mathematics, Ukrainian Academy of Sciences, L'vov

    O. M. Mel'nik

Authors
  1. O. M. Mel'nik
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 1, pp. 69–77, January, 1993.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mel'nik, O.M. Construction of unital matrix polynomials with mutually distinct characteristic roots. Ukr Math J 45, 76–84 (1993). https://doi.org/10.1007/BF01062040

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01062040

Keywords

Search

Navigation