Liesen, Jörg2021-12-172021-12-172006-06-012197-8085https://depositonce.tu-berlin.de/handle/11303/15597http://dx.doi.org/10.14279/depositonce-14370Results of Benzi and Simoncini (Numer. Math. 103 (2006), pp.~173--196) on spectral properties of block $2\times 2$ matrices are generalized to the case of a symmetric positive semidefinite block at the (2,2) position. More precisely, a sufficient condition is derived when a (nonsymmetric) saddle point matrix of the form $[A\;\;B^T; -B\;C]$ with $A=A^T>0$, full rank $B$, and $C=C^T\geq 0$, is diagonalizable and has real and positive eigenvalues.en510 Mathematiksaddle point problemeigenvaluesStokes problemnormal matricesResearch Paper