Volume 60, pp. 276-291, 2024.

Spectral properties of certain nonsymmetric saddle point matrices

Jörg Liesen and Justus Ramme


We consider certain (real) nonsymmetric matrices in saddle point form, study their general Jordan normal forms, and prove new conditions so that these matrices are diagonalizable with a real spectrum. For matrices satisfying our conditions we show how to construct an inner product in which these matrices are selfadjoint. Our approach generalizes previously published results in this area, which require stronger assumptions on the given saddle point matrices and hence are less widely applicable.

Full Text (PDF) [590 KB], BibTeX

Key words

saddle point problems, eigenvalues and eigenvectors, conjugate gradient iterations, Krylov subspace methods

AMS subject classifications

15A18, 65F10

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