On the Stability of P-Matrices

Tang, A. and Simsek, Alp and Ozdaglar, Asuman and Acemoglu, Daron (2006) On the Stability of P-Matrices. Technical Report. California Institute of Technology, Pasadena, CA. [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.

EPrint Type:	Monograph (Technical Report)
Additional Information:	We thank Dr. Lachlan Andrew of Caltech for helpful discussions.
Subjects:	All Records
ID Code:	561
Deposited By:	Dr Ao Tang
Deposited On:	13 November 2006
Record Number:	CaltechCSTR:2006.005
Official 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.

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