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《山东大学学报(理学版)》 ›› 2026, Vol. 61 ›› Issue (2): 20-25.doi: 10.6040/j.issn.1671-9352.0.2024.392

• • 上一篇    

*-Sylvester矩阵方程转换为广义Sylvester矩阵方程的方法

汪秋分,马昌凤*   

  1. 厦门工学院人工智能学院, 福建 厦门 361021
  • 发布日期:2026-02-13
  • 通讯作者: 马昌凤(1962— ),男,教授,博士,研究方向数值代数及其应用. E-mail:mcf@fzfu.edu.cn
  • 作者简介:汪秋分(1987— ),男,副教授,硕士,研究方向数值代数. E-mail:356672150@qq.com*通信作者:马昌凤(1962— ),男,教授,博士,研究方向数值代数及其应用. E-mail:mcf@fzfu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(12371378);福建省自然科学基金项目(2023J011127);厦门工学院基于大数据的模糊系统理论及其应用科研创新团队项目(KYTD202005)

Method of transforming the *-Sylvester matrix equation into the generalized Sylvester matrix equation

WANG Qiufen, MA Changfeng*   

  1. School of Artificial Intelligence, Xiamen Institute of Technology, Xiamen 361021, Fujian, China
  • Published:2026-02-13

摘要: 研究*-Sylvester矩阵方程AX+X*B=D的等价转换形式。利用Kronecker积和向量化算子以及置换矩阵的基本性质,分离了矩阵的实部和虚部,在两种不同的情况下得到了*-Sylvester矩阵方程的等价转换形式,并证明了在满足一定条件下其可以等价转换为广义Sylvester矩阵方程。

关键词: *-Sylvester矩阵方程, 广义 Sylvester矩阵方程, Kronecker积, 向量化, 等价转换

Abstract: The equivalent transformation form of the *-Sylvester matrix equation AX+X*B=D is studied. Using the basic properties of Kronecker product, vectorization operator and permutation matrix,and separating the real and imaginary parts of the matrix, we obtain the equivalent transformation form of the *-Sylvester matrix equation in two different cases. It is proved that it can be equitably converted to generalized Sylvester matrix equation under certain conditions.

Key words: *-Sylvester matrix equation, generalized Sylvester matrix equation, Kronecker product, vectorization, equivalent transformation

中图分类号: 

  • O241
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