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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2014, Number 3, Pages 38–48
(Mi basm368)
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Equivalence of pairs of matrices with relatively prime determinants over quadratic rings of principal ideals
Natalija Ladzoryshyn, Vasyl' Petrychkovych Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of the NAS of Ukraine, 3b Naukova Str., 79060, L'viv, Ukraine
Abstract:
A special equivalence of matrices and their pairs over quadratic rings is investigated. It is established that for the pair of $n\times n$ matrices $A,B$ over the quadratic rings of principal ideals $\mathbb Z[\sqrt k]$, where $(\operatorname{det}A,\operatorname{det}B)=1$, there exist invertible matrices $U\in GL(n,\mathbb Z)$ and $V^A,V^B\in GL(n,\mathbb Z[\sqrt k])$ such that $UAV^A=T^A$ and $UBV^B=T^B$ are the lower triangular matrices with invariant factors on the main diagonals.
Keywords and phrases:
quadratic ring, matrices over quadratic rings, equivalence of pairs of matrices.
Received: 30.05.2014
Citation:
Natalija Ladzoryshyn, Vasyl' Petrychkovych, “Equivalence of pairs of matrices with relatively prime determinants over quadratic rings of principal ideals”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2014, no. 3, 38–48
Linking options:
https://www.mathnet.ru/eng/basm368 https://www.mathnet.ru/eng/basm/y2014/i3/p38
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Abstract page: | 152 | Full-text PDF : | 52 | References: | 16 |
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