A condition for the nonsymmetric saddle point matrix being diagonalizable and having real and positive eigenvalues

摘要

This paper discusses the spectral properties of the nonsymmetric saddle point matrices of the form A=[ABT;-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].