四元数矩阵方程组AXB=C,DXE=F通解复分量的极秩  

Extremal Ranks of Complex Matrices in General Solutions of the System of Quaternion Matrix Equations AXB=C,DXE=F

作　　者：吴恒飞 张宗标 WU Heng-fei;ZHANG Zong-biao(Bozhou College Department of Electronic and Information Engineering,Bozhou 236800,China)

机构地区：[1]亳州学院电子与信息工程系,安徽亳州236800

出　　处：《数学的实践与认识》2021年第16期235-244,共10页Mathematics in Practice and Theory

基　　金：安徽省高校自然科学研究项目(KJ2017A704,KJ2016A492,KJ2020A0773);亳州学院重点科研项目(BYZ2019B03)。

摘　　要：利用四元数矩阵的复表示把矩阵方程组AXB=C,DXE=F变成等价的复矩阵方程组,给出等价方程组的通解.利用四元数矩阵复表示的性质、分块矩阵秩的性质和分块矩阵变换,得到方程组通解的复分量的极大秩,极小秩公式.作为应用,给出方程组特殊解的充要条件以及方程组特殊条件时的极大秩、极小秩公式.By using the complex representation of the quaternion matrix,the equations AXB= C,DXE=F are transformed into equivalent complex matrix equations,and its expressions of the general solution is given;maximal and minimal ranks of the complex component in general solution are obtained from the property of the quaternion matrix complex representation,the property of the rank of the block matrix,and the block matrix transformation;as an application,the necessary and sufficient conditions for the special solution of the equation system and the maximum rank and minimum rank formulas for the special conditions of the equation system are given.

关 键 词：四元数矩阵方程组 复分量 极大秩 极小秩 分块矩阵 

分 类 号：O151.21[理学—数学]