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On the Stability of P-Matrices

Tang, A. Kevin and Simsek, Alp and Ozdaglar, Asuman and Acemoglu, Daron (2006) On the Stability of P-Matrices. Computer Science Technical Reports, 2006.004. California Institute of Technology , Pasadena, CA. (Unpublished)

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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)
Tang, A. Kevin0000-0001-6296-644X
Additional Information:We thank Dr. Lachlan Andrew of Caltech for helpful discussions.
Group:Computer Science Technical Reports
Record Number:CaltechCSTR:2006.005
Persistent URL:
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
Deposited By: Imported from CaltechCSTR
Deposited On:13 Nov 2006
Last Modified:13 Mar 2018 21:17

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