On the Divisibility of Matrices with Remainder over the Domain of Principal Ideals


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We study the problem of divisibility of matrices with remainder over a domain of principal ideals R and establish the conditions under which, for a pair of (n × n)-matrices A and B over the domain R , there exists a unique pair of (n × n)-matrices P and Q over R such that B = AP +Q. The application of the obtained results to finding special solutions of a Sylvester-type matrix equation is presented.

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V. Prokip

Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, Ukrainian National Academy of Sciences

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乌克兰, Lviv

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