Dominant matrices and max algebra

0351435 - ÚI 2011 RIV US eng J - Journal Article
Fiedler, Miroslav
Dominant matrices and max algebra.
Linear Algebra and Its Applications. Roč. 434, č. 4 (2011), s. 1189-1194. ISSN 0024-3795. E-ISSN 1873-1856
Institutional research plan: CEZ:AV0Z10300504
Keywords : totally positive matrix * factorization * Monge matrix * (0,1) matrix
Subject RIV: BA - General Mathematics
Impact factor: 0.974, year: 2011

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
Permanent Link: http://hdl.handle.net/11104/0191192