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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2023, Vol. 40 ›› Issue (3): 456-470.doi: 10.3969/j.issn.1005-3085.2023.03.009

• • 上一篇    下一篇

一类四元数矩阵方程组的中心对称解及其极秩

王  云,   黄敬频   

  1. 广西民族大学数学与物理学院，南宁 530006
  • 收稿日期:2021-01-16 接受日期:2021-06-08 出版日期:2023-06-15 发布日期:2023-08-15
  • 通讯作者: 黄敬频 E-mail: hjp2990@126.com
  • 基金资助:
    国家自然科学基金 (11661011)；广西民族大学研究生创新项目 (gxun-chxzs2019025).

Centrosymmetric Solution to a Class of Quaternion Matrix Equations and Its Extremal Ranks

WANG Yun,  HUANG Jingpin   

  1. College of Mathematics and Physics, Guangxi Minzu University, Nanning 530006
  • Received:2021-01-16 Accepted:2021-06-08 Online:2023-06-15 Published:2023-08-15
  • Contact: J. Huang. E-mail address: hjp2990@126.com
  • Supported by:
    The National Natural Science Foundation of China (11661011); the Innovation Project of Graduate Education of Guangxi Minzu University (gxun-chxzs2019025).

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摘要：

研究一类四元数矩阵方程组存在中心对称解的充要条件及其通解的极秩问题。利用中心对称矩阵的特征结构，将该约束方程组转化为等价的无约束矩阵方程组的求解问题，然后采用M-P广义逆和分块矩阵秩的刻画方法，获得原方程组的中心对称解的表达式以及其极秩。所得定理推广了有关文献的结果。

关键词: 四元数矩阵方程组, 心对称矩阵, 分块矩阵, M-P广义逆, 极秩

Abstract:

Investigated are the centrosymmetric matrix solution for a system of quaternion matrix equations and its extremal ranks. By using the properties of centrosymmetric matrix and M-P generalized inverse, a constrained problem is transformed into unconstrained equations. The necessary and sufficient conditions for the equations with centrosymmetric matrix solutions as well as their extremal rank are obtained. The obtained conclusions extend the results of related literature.

Key words: quaternion matrix equations, centrosymmetric matrix, block matrix, M-P generalized inverse, extremal rank

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