Solutions of the matrix linear bilateral polynomial equation and their structure

• Datum: 2019
• Hauptverfasser: Dzhaliuk, Nataliia S., Petrychkovych, Vasyl' M.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Lugansk National Taras Shevchenko University 2019
• Schlagworte: matrix polynomial equation; solution; polynomial matrix; semiscalar equivalence; 15A21; 15A24
• Online Zugang: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1210
• Назва журналу: 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...