On the Stability of P-Matrices

Abstract

We establish two sufficient conditions for the stability of a P-matrix. First, we show that a P-matrix is positive stable if its skew-symmetric component is sufficiently smaller (in matrix norm) than its symmetric component. This result generalizes the fact that symmetric P-matrices are positive stable, and is analogous to a result by Carlson which shows that sign symmetric P-matrices are positive stable. Second, we show that a P-matrix is positive stable if it is strictly row (column) square diagonally dominant for every order of minors. This result generalizes the fact that strictly row diagonally dominant P-matrices are stable. We compare our sufficient conditions with the sign symmetric condition and demonstrate that these conditions do not imply each other.