Cover Image

On One Class of Divisors of Polynomial Matrices over Integral Domains

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.

Saved in:

Bibliographic Details
Date:	2003
Main Authors:	Prokip, V. M., Прокіп, В. М.
Format:	Article
Language:	Ukrainian English
Published:	Institute of Mathematics, NAS of Ukraine 2003
Online Access:	https://umj.imath.kiev.ua/index.php/umj/article/view/3984
Tags:	Add Tag No Tags, Be the first to tag this record!
Journal Title:	Ukrains’kyi Matematychnyi Zhurnal
Download file:

Institution

Ukrains’kyi Matematychnyi Zhurnal

Similar Items

Structure of Matrices and Their Divisors over the Domain of Principal Ideals
by: Prokip, V. M., et al.
Published: (2002)

On the factorization of polynomial matrices over the domain of principal ideals
by: Prokip, V. M., et al.
Published: (1996)

Polynomial matrices over a factorial domain and their factorization with given characteristic polynomials
by: Prokip, V. M., et al.
Published: (1998)

On the uniqueness of the unital divisor of a matrix polynomial over an arbitrary field
by: Prokip, V. M., et al.
Published: (1993)

On the equivalence of polynomial matrices over a field
by: Prokip , V., et al.
Published: (2024)

Factorization of matrices over elementary divisor domain
by: Shchedryk, V.
Published: (2009)

Factorization of matrices over elementary divisor domain
by: Shchedryk, Volodymyr
Published: (2018)

Diagonalizability of matrices over a principal ideal domain
by: Prokip, V. M., et al.
Published: (2012)

Monic divisors of polynomial matrices over infinite field
by: Romaniv, Andriy
Published: (2018)

On Multiplicativity of Canonical Diagonal Forms of Matrices over the Domain of Principal Ideals. II
by: Prokip, V. M., et al.
Published: (2001)

To the problem of multiplicativity of canonical diagonal forms of matrices over the domain of principal ideals
by: Prokip, V. M., et al.
Published: (1995)

A method for finding a common linear divisor of the matrix polynomials over an arbitrary field
by: Prokip, V. M., et al.
Published: (1993)

Triangularization of a pair of matrices over a principal ideal domain with minimal quadratic polynomials
by: V. M. Prokip
Published: (2015)

The structure of matrices of rank one over the domain of principal ideals with respect to similarity transformation
by: V. M. Prokip
Published: (2016)

On the equivalence of polynomial matrices over a field
by: V. Prokip
Published: (2024)

Principal flat ideals in the ring of matrices over commutative elementary divisors domain
by: H. V. Zelisko
Published: (2012)

On the Smith normal form of the greatest common divisor of one class of matrices
by: A. M. Romaniv
Published: (2015)

The greatest common divisors and least common multiples of matrices over commutative Bezout domains
by: V. P. Shchedryk
Published: (2014)

The least common multiple of matrices from one class of matrices over a commutative principal ideal domain
by: A. M. Romaniv
Published: (2017)

On divisibility with a remainder of matrices over a principal ideal domain
by: V. M. Prokip
Published: (2017)

On normal form with respect to semiscalar equivalence of polynomial matrices over a field
by: V. M. Prokip
Published: (2012)

Canonical form of polynomial matrices with all identical elementary divisors
by: Shavarovskyy, B. Z., et al.
Published: (2012)

The canonical form of involutory matrices over the principal ideal domain with respect to similarity transformation
by: V. M. Prokip
Published: (2019)

Stable rank of the set of full matrices over the ring of elementary divisors
by: B. V. Zabavskyi, et al.
Published: (2014)

On the Solvability of a System of Linear Equations Over the Domain Of Principal Ideals
by: Prokip, V. M., et al.
Published: (2014)

Greatest common divisor of matrices one of which is a disappear matrix
by: Romaniv, A. M., et al.
Published: (2014)

Greatest common divisor of matrices one of which is a disappear matrix
by: O. M. Romaniv, et al.
Published: (2014)

Generalized equivalence of collections of matrices and common divisors of matrices
by: Petrychkovych, V.M.
Published: (2004)

Generalized equivalence of collections of matrices and common divisors of matrices
by: Petrychkovych, Vasyl M.
Published: (2018)

Diagonalizability theorem for matrices over certain domains
by: Zabavsky, B., et al.
Published: (2011)

A criterion of elementary divisor domain for distributive domains
by: V. Bokhonko, et al.
Published: (2017)

Generated set of matrices divisors and its propertiess
by: V. P. Shchedryk
Published: (2013)

A criterion of elementary divisor domain for distributive domains
by: Bokhonko, Vasylyna, et al.
Published: (2017)

Some relationships between the invariant factors of matrix and its submatrix over elementary divisor domains
by: A. M. Romaniv, et al.
Published: (2019)

Some relationships between the invariant factors of matrix and its submatrix over elementary divisor domains
by: Romaniv, A. M.; Романів А. М.; Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України, Львів, et al.
Published: (2019)

The left greatest common divisor and the left least common multiple of all solutions of the matrix equation BX = A over a commutative elementary divisor domain
by: Shchedryk, V. P., et al.
Published: (2021)

On one class of partition polynomials
by: R. Zatorsky, et al.
Published: (2013)

A note to my paper “Generalized equivalence of collections of matrices and common divisors of matrices”
by: Petrychkovych, V.M.
Published: (2005)

The left greatest common divisor and the left least common multiple of all solutions of the matrix equation BX = A over a commutative elementary divisor domain
by: V. P. Shchedryk
Published: (2021)

Non-singular solutions of one class of matrix equations over a polynomial ring
by: B. Z. Shavarovskyi
Published: (2019)