Abstract

Let \(A\) be a complex \(n \times n\) matrix. The set \(\mathcal{L}\) of matrices \(X\) satisfying the relation \({{X}^{T}}AX = A\) is called the \(T\)-congruence centralizer of \(A\). It is shown that the calculation of matrices from the nonlinear variety \(\mathcal{L}\) can be reduced to solving a linear matrix equation.

中文翻译：

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关于T同余扶正器的计算。

摘要

令\（A \）为复数\（n \ times n \）矩阵。该组\（\ mathcal {L} \）矩阵\（X \）满足关系\（{{X} ^ {T】} AX = A \）被称为\（T \） -同余扶正\ （A \）。结果表明，可以将非线性变种\（\ mathcal {L} \）的矩阵计算简化为线性矩阵方程的求解。