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.

中文翻译：

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同时空心化、联合数值范围和噪声稳定

我们将任意方阵的正交变换考虑为所有对角线项都相等的形式。在我们的主要结果中，我们处理两个矩阵的同时变换和一个矩阵的辛正交变换。计算了联合实数值范围的关系，开发了有效的数值算法，并提出了通过旋转和噪声稳定的应用。