Abstract
It is required to separate a unital divisor with a preassigned characteristic polynomial from a rectangular polynomial matrix over a field. Necessary and sufficient conditions of existence, under certain restrictions, are obtained for such a divisor, as well as a method for constructing it. By the approach used in this paper it is possible to completely solve this problem for rectangular polynomial matrices, all of whose elementary divisiors are pair-wise relatively prime. The results obtained are illustrated by solving matrix equations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
P. S. Kazimirs'kii, Factorization of Matrix Polynomials [in Ukrainian], Naukova Dumka, Kiew (1981).
A. N. Malyshev, “Factorization of matrix polynomials,” Sib. Mat. Zh.,23, No. 3, 136–146 (1982).
I. Gohberg, P. Lancaster, and L. Rodman, Matrix Polynomials, Acad. Press, New York-London (1982).
V. M. Petrichkovich and V. M. Prokip, “Factorization of polynomial matrices over a field,” Ukr. Mat. Zh.,38, No. 4, 478–483 (1986).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 8, pp. 1089–1094, August, 1990.
Rights and permissions
About this article
Cite this article
Prokip, V.M. Separating a unital divisor from a rectangular polynomial matrix. Ukr Math J 42, 971–976 (1990). https://doi.org/10.1007/BF01099230
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01099230