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On the Stability of P-Matrices

Tang, A. and Simsek, Alp and Ozdaglar, Asuman and Acemoglu, Daron (2006) On the Stability of P-Matrices. California Institute of Technology , Pasadena, CA. (Submitted) http://resolver.caltech.edu/CaltechCSTR:2006.005

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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.


Item Type:Report or Paper (Technical Report)
Additional Information:We thank Dr. Lachlan Andrew of Caltech for helpful discussions.
Group:Computer Science Technical Reports
Record Number:CaltechCSTR:2006.005
Persistent URL:http://resolver.caltech.edu/CaltechCSTR:2006.005
Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:27082
Collection:CaltechCSTR
Deposited By: Imported from CaltechCSTR
Deposited On:13 Nov 2006
Last Modified:26 Dec 2012 14:14

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