Calculation of the eigenvectors of two- and three-dimensional coherency matrices, and the four-dimensional coherency matrix associated with a Mueller matrix, is considered, especially for algebraic cases, in the light of recently published algorithms. The preferred approach is based on a combination of an evaluation of the characteristic polynomial and an adjugate matrix. The diagonal terms of the coherency matrix are given in terms of the characteristic polynomial of reduced matrices as functions of the eigenvalues of the coherency matrix. The analogous polynomial form for the off-diagonal elements of the coherency matrix is also presented. Simple expressions are given for the pure component in the characteristic decomposition.

中文翻译：

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极化相干矩阵的特征向量。

根据最近发表的算法，尤其是在代数情况下，考虑了二维和三维相干矩阵的特征向量的计算以及与Mueller矩阵相关联的三维相干矩阵的计算。优选的方法基于特征多项式的评估和辅助矩阵的组合。相干矩阵的对角项是根据归约矩阵特征值的归约矩阵的特征多项式给出的。还介绍了相干矩阵的非对角线元素的类似多项式形式。对于特征分解中的纯组分给出了简单的表达式。