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Triangular form of Laurent polynomial matrices and their factorization

MMC.
2022;
Volume 9, Number 1
: pp. 119–129
https://doi.org/10.23939/mmc2022.01.119
Received: August 01, 2021
Revised: December 15, 2021
Accepted: December 19, 2021

Mathematical Modeling and Computing, Vol. 9, No. 1, pp. 119–129 (2022)

Authors:
  1. M. I. Kuchma
  2. A. I. Gatalevych
1
Lviv Polytechnic National University
2
Ivan Franko National University of Lviv

The issue of the semiscalar equivalence of Laurent polynomial matrices is investigated and the triangular form of such matrices and their finite sets is established with respect to this equivalence.  The theorem on regularization of a Laurent polynomial matrix is proved.  This theorem is used in the problem of factorization of such matrices.  The factorization criterion of a Laurent polynomial matrix with a regular multiplier with a predetermined Smith normal form is obtained.

Laurent polynomial matrix
semiscalar equivalence
triangular form
Smith normal form
matrix factorization
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