O. O. Shchekaturova, V. A. Yaroshevich, “On the properties of Boolean matrices”, Izv. Saratov Univ. Math. Mech. Inform., 2013, Volume 13, Issue 4(2),Pages <nobr>137

This article is cited in 1 paper

Mathematics

On the properties of Boolean matrices

O. O. Shchekaturova^a, V. A. Yaroshevich^b

^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

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.

UDC: 512.554+512.643

DOI: 10.18500/1816-9791-2013-13-4-137-142