Johnson, Charles R.; Stanford, David P. Qualitative semipositivity. (English) Zbl 0791.15016 Brualdi, Richard A. (ed.) et al., Combinatorial and graph-theoretical problems in linear algebra. Proceedings of a workshop that was an integral part of the 1991-92 IMA program on “Applied Linear Algebra” held at the University of Minnesota, USA, November 11-15, 1991. New York: Springer-Verlag. IMA Vol. Math. Appl. 50, 99-105 (1993). A real \(m \times n\) matrix \(A\) is called semipositive (SP) if there is a real \(n\)-vector \(x \geq 0\) such that \(Ax>0\). A semipositive matrix \(A\) is called minimally semipositive (MSP) provided no matrix obtained from \(A\) by deleting one or more columns is semipositive. A semipositive matrix that is not MSP is called redundantly semipositive (RSP).The authors study SP, MSP and RSP from the standpoint of qualitative matrix theory; that is, the study of the sign patterns that require or allow a given property. A characterisation is given in each of the three cases.For the entire collection see [Zbl 0780.00017]. Reviewer: Eugene Seneta (Sydney) Cited in 4 Documents MSC: 15B48 Positive matrices and their generalizations; cones of matrices Keywords:minimally semipositive matrix; redundantly semipositive matrix; sign patterns PDFBibTeX XMLCite \textit{C. R. Johnson} and \textit{D. P. Stanford}, IMA Vol. Math. Appl. 50, 99--105 (1993; Zbl 0791.15016)