*-Sylvester矩阵方程转换为广义Sylvester矩阵方程的方法

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

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。

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.

关键词

*-Sylvester矩阵方程 / 广义Sylvester矩阵方程 / Kronecker积 / 向量化 / 等价转换

Key words

*-Sylvester matrix equation / generalized Sylvester matrix equation / Kronecker product / vectorization / equivalent transformation

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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)