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.
