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

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 AA 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].