Letter to the Editor: A condition for the nonsymmetric saddle point matrix being diagonalizable and having real and positive eigenvalues

Authors:
Shu-Qian Shen;Ting-Zhu Huang;Guang-Hui Cheng
Affiliations:
School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, PR China;School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, PR China;School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 3
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Abstract

This paper discusses the spectral properties of the nonsymmetric saddle point matrices of the form A=[AB^T;-BC] with A symmetric positive definite, B full rank, and C symmetric positive semidefinite. A new sufficient condition is obtained so that A is diagonalizable with all its eigenvalues real and positive. This condition is weaker than that stated in the recent paper [J. Liesen, A note on the eigenvalues of saddle point matrices, Technical Report 10-2006, Institute of Mathematics, TU Berlin, 2006].