A Note on the Eigenvalues of Saddle Point Matrices

The spectral properties of saddle point matrices arising from saddle point problems are discussed. The relations of the eigenvalues and the determinants between the saddle point matrices and their sub blocks are investigated. An appropriate estimate on the maximum eigenvalue of saddle point matrix is given. In the numerical experiment the saddle point matrices derived from the mixed finite element discretizations on Stokes equation are observed. Numerical results confirm the theoretical analysis and demonstrate that the estimate on the maximum eigenvalue of saddle point matrix is proper.