Solutions of the matrix linear bilateral polynomial equation and their structure

• Date: 2019
• Main Authors: Dzhaliuk, Nataliia S., Petrychkovych, Vasyl' M.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2019
• Subjects: matrix polynomial equation; solution; polynomial matrix; semiscalar equivalence; 15A21; 15A24
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1210
• Journal Title: Algebra and Discrete Mathematics

We investigate the row and column structure of solutions of the matrix polynomial equation \[ A(\lambda)X(\lambda)+Y(\lambda)B(\lambda)=C(\lambda), \] where \(A(\lambda)\), \(B(\lambda)\) and \(C(\lambda)\) are the matrices over the ring of polynomials \(\mathcal{F}[\lambda]\) with coefficients in f...