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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].

MSC:

15B48 Positive matrices and their generalizations; cones of matrices
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