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.

We thank Dr. Lachlan Andrew of Caltech for helpful discussions.

Submitted - Pmatrix5.pdf