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Algebra and Discrete Mathematics, 2004, Issue 2, Pages 84–91
(Mi adm340)
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RESEARCH ARTICLE
Generalized equivalence of collections of matrices and common divisors of matrices
Vasyl' M. Petrychkovych Department of Algebra, Pidstryhach Institute
for Applied Problems of Mechanics and
the Mathematics National Academy of Sciences
of Ukraine, 3B Naukova Str., Lviv, 9053, Ukraine
Abstract:
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 the finite collection consisting of the matrix and its the divisors is generalized equivalent to the collection of the matrices of the triangular and diagonal forms. By using these forms the common divisors of matrices is described.
Keywords:
collection of matrices, generalized equivalence, canonical diagonal form, common divisors.
Received: 21.04.2004 Revised: 25.05.2004
Citation:
Vasyl' M. Petrychkovych, “Generalized equivalence of collections of matrices and common divisors of matrices”, Algebra Discrete Math., 2004, no. 2, 84–91
Linking options:
https://www.mathnet.ru/eng/adm340 https://www.mathnet.ru/eng/adm/y2004/i2/p84
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Abstract page: | 119 | Full-text PDF : | 51 | First page: | 1 |
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