Generalized equivalence of collections of matrices and common divisors of matrices

• Date: 2018
• Main Author: Petrychkovych, Vasyl M.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: collection of matrices; generalized equivalence; canonical diagonal form; common divisors; 15A33; 15A21; 15A23
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/992
• Journal Title: Algebra and Discrete Mathematics

The collections  \((A_{1}, ..., A_{k})\) and \((B_{1}, ..., B_{k})\) of matrices over an adequate ring are called generalized equivalent  if \(A_i=UB_iV_i\) for some invertible matrices \(U\) and \(V_{i}, \; i=1, ..., k.\) Some conditions are established under which the finite collection  consisting...