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Characterizations of minimal semipositivity. (English) Zbl 0815.15017

A real \(m \times n\) matrix \(A\) is semipositive if there is a real \(n\)- vector \(x \geq 0\) such that \(Ax > 0\). \(A\) is minimally semipositive if it is semipositive and no proper submatrix of \(A\) obtained by deleting only columns is semipositive. Minimal semipositivity is characterized and is related to rectangular monotonicity and weak \(r\)-monotonicity. \(P_ +\)- matrices and nonnegative matrices are also considered.
Reviewer: G.Bonanno (Davis)

MSC:

15B48 Positive matrices and their generalizations; cones of matrices
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