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Simultaneous Hollowization, Joint Numerical Range, and Stabilization by Noise

: Damm, T.; Faßbender, H.


SIAM journal on matrix analysis and applications 41 (2020), Nr.2, S.637-656
ISSN: 0196-5212
ISSN: 1095-7162
Fraunhofer ITWM ()

We consider orthogonal transformations of arbitrary square matrices to a form where all diagonal entries are equal. In our main results we treat the simultaneous transformation of two matrices and the symplectic orthogonal transformation of one matrix. A relation to the joint real numerical range is worked out, efficient numerical algorithms are developed, and applications to stabilization by rotation and by noise are presented.