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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2013, Volume 13, Issue 4(2), Pages 137–142
DOI: https://doi.org/10.18500/1816-9791-2013-13-4-137-142 (Mi isu477) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

On the properties of Boolean matrices

O. O. Shchekaturovaa, V. A. Yaroshevichb

a Saratov State University, Russia, 410012, Saratov, Astrakhanskaya st., 83
b National Research University of Electronic Technology (MIET), Russia, 124498, Moscow, Zelenograd, pass. 4806, 5
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DOI: https://doi.org/10.18500/1816-9791-2013-13-4-137-142
Abstract: We consider the partial semigroup of Boolean matrices of various finite sizes under the operations of conjunctive and disjoint multiplication. We estimate the possible number of vectors in the row basis and column basis. The subminimal, subsubminimal and submaximal in general sense $\mathscr D$-classes are found. The properties of secondary idempotents are investigated. A conjecture of recursive construction of the reduced matrices is suggested.
Key words: Boolean matrix, conjunctive product, disjoint product, row span, column span, row rank, column rank, reduced matrix, Green's classes, primary idempotent, secondary idempotent.
Bibliographic databases:
Document Type: Article
UDC: 512.554+512.643
Language: Russian
Citation: O. O. Shchekaturova, V. A. Yaroshevich, “On the properties of Boolean matrices”, Izv. Saratov Univ. Math. Mech. Inform., 13:4(2) (2013), 137–142
Citation in format AMSBIB
\Bibitem{ShcYar13}
\by O.~O.~Shchekaturova, V.~A.~Yaroshevich
\paper On the properties of Boolean matrices
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2013
\vol 13
\issue 4(2)
\pages 137--142
\mathnet{http://mi.mathnet.ru/isu477}
\crossref{https://doi.org/10.18500/1816-9791-2013-13-4-137-142}
\elib{https://elibrary.ru/item.asp?id=21976921}
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