On the stability of P-matrices

✍ Scribed by A. Kevin Tang; Alp Simsek; Asuman Ozdaglar; Daron Acemoglu

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 180 KB
• Volume: 426
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2007.03.034

✦ Synopsis

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.