Simultaneous hollowisation, joint numerical range, and stabilization by noise

10/19/2019

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by   Tobias Damm, et al.

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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 developped and applications to stabilization by rotation and by noise are presented.