不定内积空间中四元数矩阵的极性分解

IF 0.7 4区数学 Q2 Mathematics

Electronic Journal of Linear Algebra Pub Date : 2021-06-19 DOI:10.13001/ela.2021.6411

G. Groenewald, D.B. Janse van Rensburg, A. Ran, F. Theron, M. Van Straaten

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引用次数: 0

摘要

研究了给定不定内积四元数矩阵的极坐标分解问题。给出了H -极分解存在的充分必要条件。在此过程中，对于四元数矩阵，给出了将$H$-等距扩展到$H$-酉矩阵的一个等价的Witt定理。

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Polar decompositions of quaternion matrices in indefinite inner product spaces

Polar decompositions of quaternion matrices with respect to a given indefinite inner product are studied. Necessary and sufficient conditions for the existence of an $H$-polar decomposition are found. In the process, an equivalent to Witt's theorem on extending $H$-isometries to $H$-unitary matrices is given for quaternion matrices.

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来源期刊

Electronic Journal of Linear Algebra 数学-数学

CiteScore

1.20

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal is essentially unlimited by size. Therefore, we have no restrictions on length of articles. Articles are submitted electronically. Refereeing of articles is conventional and of high standards. Posting of articles is immediate following acceptance, processing and final production approval.