On solvability of the matrix equation AXB = C  over a principal ideal domain

Volodymyr Prokip

doi:10.31713/MCIT.2020.09

On solvability of the matrix equation AXB = C over a principal ideal domain

Authors

Volodymyr Prokip Pidstryhach Institute for Applied Problems of Mechanics and Mathematics NAS of Ukraine https://orcid.org/0000-0001-5539-7904

DOI:

https://doi.org/10.31713/MCIT.2020.09

Keywords:

matrix equation, solution, domain of principal ideal

Abstract

In this paper we present conditions of solvability of the matrix equation AXB = B over a principal ideal domain. The necessary and sufficient conditions of solvability of equation AXB = B in term of the Smith normal forms and in term of the Hermi-te normal forms of matrices constructed in a certain way by using the coefficients of this equation are proposed. If a solution of this equation exists we propose the method for its construction.

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Published

2020-10-22

How to Cite

Prokip, V. (2020). On solvability of the matrix equation AXB = C over a principal ideal domain. Modeling, Control and Information Technologies, (4), 47–50. https://doi.org/10.31713/MCIT.2020.09

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Issue

No. 4 (2020): Modeling, control and information technologies

Section

Mathematical, computer modeling and computational methods

License

All materials are distributed under the terms of the Creative Commons Attribution 4.0 International License, which allows others to distribute the work with attribution to the authorship of this work and the first publication in this journal.