四元数矩阵方程 AX+ X ∗ B+CY=D的三对角广义(反)对称解  

Tridiagonal Generalized (Skew-) Symmetric Solution for the Quaternion Matrix Equation AX+ X ∗ B+CY=D

作　　者：王梓沣 张澜[1] 

机构地区：[1]内蒙古工业大学理学院,内蒙古 呼和浩特

出　　处：《应用数学进展》2025年第2期251-262,共12页Advances in Applied Mathematics

基　　金：国家自然科学基金(12261065)和内蒙古自治区自然科学基金项目(2023LHMS01016)。

摘　　要：文章对于给定的四元数矩阵A,B,C和D,深入讨论了矩阵方程AX+X∗B+CY=D的三对角广义(反)对称解。利用Kronecker积,矩阵拉直算子以及Moore-Penrose广义逆等理论,充分考虑三对角广义(反)对称矩阵的结构特点,讨论了四元数矩阵方程三对角广义(反)对称解的结果,给出方程有解的充分必要条件及解的表达式。This paper discusses in depth the tridiagonal generalized (skew-) symmetric solutions for the given quaternion matrices A,B,C, and Din the matrix equation AX+X∗B+CY=D. By employing the theories of the Kronecker product, matrix vectorization, and the Moore-Penrose generalized inverse, the research thoroughly considers the structural characteristics of tridiagonal generalized (skew-) symmetric matrices. It discusses the outcomes of the quaternion matrix equation’s tridiagonal generalized (skew-) symmetric solutions, provides the necessary and sufficient conditions for the equation to have a solution, and presents the expressions for these solutions.

关 键 词：四元数矩阵 KRONECKER积 MOORE-PENROSE广义逆 三对角广义(反)对称矩阵 

分 类 号：O17[理学—数学]