Table of Contents Author Guidelines Submit a Manuscript
International Journal of Analysis
Volume 2017 (2017), Article ID 2867354, 7 pages
Research Article

The Structure of Symmetric Solutions of the Matrix Equation over a Principal Ideal Domain

Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Naukova Str. 3b, L’viv, Ukraine

Correspondence should be addressed to V. M. Prokip

Received 20 June 2017; Accepted 18 September 2017; Published 5 November 2017

Academic Editor: Fatemeh P. Ali Beik

Copyright © 2017 V. M. Prokip. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We investigate the structure of symmetric solutions of the matrix equation , where and are -by- matrices over a principal ideal domain and is unknown -by- matrix over . We prove that matrix equation over has a symmetric solution if and only if equation has a solution over and the matrix is symmetric. If symmetric solution exists we propose the method for its construction.