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Dominant matrices and max algebra
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SYSNO ASEP 0351435 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Dominant matrices and max algebra Author(s) Fiedler, Miroslav (UIVT-O) SAI, RID Source Title Linear Algebra and Its Applications. - : Elsevier - ISSN 0024-3795
Roč. 434, č. 4 (2011), s. 1189-1194Number of pages 6 s. Language eng - English Country US - United States Keywords totally positive matrix ; factorization ; Monge matrix ; (0,1) matrix Subject RIV BA - General Mathematics CEZ AV0Z10300504 - UIVT-O (2005-2011) UT WOS 000286864300023 EID SCOPUS 78650517640 DOI 10.1016/j.laa.2010.10.029 Annotation We study the class of so-called totally dominant matrices in the usual algebra and in the max algebra in which the sum is the maximum and the multiplication is usual. It turns out that this class coincides with the well known class of positive matrices having positive the determinants of all 2×2 submatrices. The closure of this class is closed not only with respect to the usual but also with respect to the max multiplication. Further properties analogous to those of totally positive matrices are proved and some connections to Monge matrices are mentioned. Keywords: Totally positive matrix; Factorization; Monge matrix; (0,1) matrix Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2011
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