Extended M-matrices and subtangentiality (Q1094506)

This paper deals with the generalization of certain results on \({\mathcal K}\)-general (\({\mathcal K}\subset R^ n\) is a proper cone) M-matrices. The real \(n\times n\)-matrix A is called \({\mathcal K}\)-extended M-matrix (\({\mathcal K}eMm)\) if \(e^{At}{\mathcal K}\subset {\mathcal K}\), \(t\in R_+\), and -A is weakly stable. Under conditions that \(e^{-At}{\mathcal K}\subset {\mathcal K}\) (instead of \({\mathcal K}\)-regularity, which is stronger) and \({\mathcal S}\underline\triangle \{int K\}\cap {\mathcal S}_ A\neq \phi ({\mathcal S}_ A\underline\triangle \cup^ m_ 0{\mathcal R}(A^ m);\) \({\mathcal R}(.)=range)\), A is a \({\mathcal K}eMm\) iff there exists \(x\in {\mathcal K}\cap {\mathcal S}_ A\) such that Ax\(\in {\mathcal S}\). In the proof the lack of regularity is overcome by using the geometric condition of subtangentiality.