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Generalized equivalence of collections of matrices and common divisors of matrices. (English) Zbl 1063.15503

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
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