Skip to main content
SpringerLink
Log in

Monic divisors with one invariant factor of polynomial matrices

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

For a nonsingular polynomial matrix over an infinite field, necessary and sufficient conditions for separation of a monic factor from a matrix polynomial with canonical diagonal form diag (1,…,1, φ(x)) are established.

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. V. R. Zelisko, “On the construction of one class of invertible matrices,” Mat. Met. Fiz.-Mekh. Polya, Issue 12, 14–21 (1980).

    Google Scholar 

  2. V. R. Zelisko and V. P. Shchedryk, “Matrix of values on a system of roots of diagonal elements of the matrix and its applications,” Mat. Met. Fiz.-Mekh. Polya, 48, No. 4, 20–29 (2005).

    MATH  Google Scholar 

  3. P. S. Kazimirskii, “A solution to the problem of separating a regular factor from a matrix polynomial,” Ukr. Math. J., 32, No. 4, 332–343 (1980).

    Article  MathSciNet  Google Scholar 

  4. A. N. Malyshev, “Factorization of matrix polynomials,” Sib. Mat. Zh., 23, No. 3, 136–146 (1982).

    MathSciNet  MATH  Google Scholar 

  5. V. M. Petrychkovych, “On the decomposability of matrix polynomials into a product of monic factors,” in: Algebra and Topology [in Ukrainian], Lviv State University, Lviv (1996), pp. 112–124.

    Google Scholar 

  6. V. P. Shchedryk, “On a class of divisors of matrices,” J. Math. Sci., 96, No. 2, 2804–2810 (1999).

    Article  Google Scholar 

  7. I. Gochberg, P. Lancaster, and L. Rodman, Matrix Polynomials, Academic Press, New York (1982).

    Google Scholar 

  8. J. Maroulas and P. Psarrakos, “On factorization of matrix polynomials,” Linear Algebra Its Appl., 304, 131–139 (2000).

    Article  MathSciNet  MATH  Google Scholar 

  9. M. Newman, Integral Matrices, Academic Press, New York (1972).

    MATH  Google Scholar 

  10. V. P. Shchedryk, “Factorization of matrices over elementary divisor rings,” Algebra Discr. Math., No. 2, 79–98 (2009).

  11. V. Shchedryk, “On decomposition of complete linear group into product of some its subgroups,” Visn. Lviv. Univ., Ser. Mekh.-Mat., Issue 61, 184–190 (2003).

  12. V. P. Shchedryk, “Some properties of primitive matrices over Bezout B -domain,” Algebra Discr. Math., No. 2, 46–57 (2005).

  13. J. Stefanovski, “Spectral factorization of non-symmetric polynomial matrices,” Linear Algebra Its Appl., 412, 412–440 (2006).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv, Ukraine

    A. M. Romaniv

Authors
  1. A. M. Romaniv
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 53, No. 4, pp. 35–43, October–December, 2010.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Romaniv, A.M. Monic divisors with one invariant factor of polynomial matrices. J Math Sci 181, 328–339 (2012). https://doi.org/10.1007/s10958-012-0688-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-012-0688-4

Keywords

Search

Navigation