Simultaneous hollowisation, joint numerical range, and stabilization by noise

2019/10/19 by Tobias Damm, Heike Faßbender, Damm, Tobias +1 · 1 citation
Computer Science · Engineering · #Matrix Theory and Algorithms #Control Systems and Identification #Digital Filter Design and Implementation

paper · pdf · doi:10.48550/arxiv.1910.08813

Abstract

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.

Citations

• Doubly Stochastic Matrices and the Diagonal of a Rotation Matrix

Cited by

• Zeroing Diagonals, Conjugate Hollowization, and Characterizing Nondefinite Operators

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