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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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|
|Usage Policy:||You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.|
|Deposited By:||Imported from CaltechCSTR|
|Deposited On:||13 Nov 2006|
|Last Modified:||26 Dec 2012 14:14|
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