Petrychkovych, Vasyl’ M. Generalized equivalence of collections of matrices and common divisors of matrices. (English) Zbl 1063.15503 Algebra Discrete Math. 2004, No. 2, 84-91 (2004). Summary: The collections \((A_1,\dots,A_k)\) and \((B_1,\dots,B_k)\) of matrices over an adequate ring are called generalized equivalent if \(A_i=UB_iV_i\) for some invertible matrices \(U\) and \(V_i,i=1,\dots,k\). Some conditions are established under which a finite collection consisting of a matrix and its divisors is generalized equivalent to a collection of matrices of the triangular and diagonal forms. By using these forms the common divisors of matrices are described. MSC: 15A21 Canonical forms, reductions, classification 15B33 Matrices over special rings (quaternions, finite fields, etc.) 15A23 Factorization of matrices Keywords:collection of matrices; generalized equivalence; canonical diagonal form; common divisors PDFBibTeX XMLCite \textit{V. M. Petrychkovych}, Algebra Discrete Math. 2004, No. 2, 84--91 (2004; Zbl 1063.15503)