四元数域中斜自共轭矩阵对角化的研究

Lieya Yan, L. Xu
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引用次数: 2

摘要

本文在斜自共轭矩阵的扩展酉对角化的基础上作了进一步的研究。从斜自共轭矩阵的定义出发,讨论了斜自共轭矩阵的一些性质,给出了判定斜自共轭矩阵是否成立的充分必要条件;是四元数域中矩阵的右特征值。利用实四元数域上的Schur定理,证明了斜自共轭可以扩展酉对角化。更进一步,如果A和B可逆且可交换,则A + B和A - 1 + B - 1可以同时扩展酉对角化。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Study of diagonalization on skew self-conjugate matrix in quaternion field
This paper made a further research based on the extended unitary diagonalization of skew self-conjugate matrix. Based on the definition of skew selfconjugate matrix, we discussed some properties of skew self-conjugate matrix, and gave the necessary and sufficient condition for determining whether ; is a right eigenvalue of matrix in the quaternion field. By means of the Schur theorem in real quaternion field, we proved that skew self-conjugate can be extended unitary diagonalized. Furthermore, if A and B are invertible and commutative, then A + B and A−1 + B−1 can be extended unitary diagonalized at the same time.
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