Ukrainian Mathematical Journal

, Volume 55, Issue 8, pp 1329–1337 | Cite as

On One Class of Divisors of Polynomial Matrices over Integral Domains

  • V. M. Prokip


We establish conditions for the existence of a unital divisor for a polynomial matrix over an integral domain of characteristic zero in the case where its eigenvalues are known.


Integral Domain Characteristic Zero Polynomial Matrix Unital Divisor 
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  1. 1.
    Ya. B. Lopatinskii, "Factorization of a polynomial matrix," Nauchn. Zap. L'vov. Politekh. Inst., Ser. Fiz. Mat., Issue 38, No. 2, 3-7 (1957).Google Scholar
  2. 2.
    P. S. Kazimirs'kyi, Factorization of Matrix Polynomials [in Ukrainian], Naukova Dumka, Kiev (1981).Google Scholar
  3. 3.
    I. Gohberg, P. Lancaster, and L. Rodman, Matrix Polynomials, Academic Press, New York (1982).Google Scholar
  4. 4.
    V. M. Prokip, "On multiplicativity of canonical diagonal forms of matrices," Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 7, 60-62 (1992).Google Scholar
  5. 5.
    M. Newman, Integral Matrices, Academic Press, New York (1972).Google Scholar
  6. 6.
    K. A. Rodosskii, Euclidean Algorithm [in Russian], Nauka, Moscow (1988).Google Scholar
  7. 7.
    V. M. Prokip, "On multiplicativity of canonical diagonal forms of matrices over the domain of principal ideals. II," Ukr. Mat. Zh., 53, No.2, 274-277 (2001).Google Scholar
  8. 8.
    V. M. Prokip, "On the solvability of linear matrix equations over a factorial domain," Visn. Univ. "L'vivs'ka Politekhnika," Ser. Prykl. Mat., No. 346, 68-72 (1998).Google Scholar
  9. 9.
    V. M. Prokip, O. M. Mel'nyk, and V. M. Kuzakon', "On one class of divisors of polynomial matrices over a field," Visn. L'viv. Nats. Univ., Ser. Prykl. Mat. Informat., Issue 5, 39-44 (2002).Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • V. M. Prokip
    • 1
  1. 1.Institute for Applied Problems in Mechanics and MathematicsUkrainian Academy of SciencesLviv

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