一个四元数矩阵方程组通解的复矩阵极秩  

Extremal Ranks of Complex Matrixs in General Solution of a Quaternion Matrix Equation System

作　　者：吴恒飞 WU Heng-fei(Department of Electronic and Information Engineering,Bozhou College,Bozhou 236800,Anhui,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：《韶关学院学报》2021年第6期1-6,共6页Journal of Shaoguan University

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

摘　　要：利用四元数矩阵复表示■(·)及其运算性质,结合分块矩阵的变换性质及其秩的性质,在复数域上讨论与四元数方程组A_(1)X=C_(1),XB_(2)=C_(2),A_(3)XB_(3)=C_(3),A_(4)XB_(4)=C_(4)等价的复矩阵方程组的通解,给出其通解的复矩阵极大秩、极小秩公式.并应用所得结论,讨论了该方程组存在纯非复解的充要条件.By using the quaternion matrix complex representation ■(·)and combining its operation properties,the transformation properties of the block matrix and the properties of the rank,the general solutions of the equivalent complex matrix equations of the quaternion equations A1X=C1,XA2=C2,A3XB3=C3,A4XB4=C4 are discussed,and its maximal and minimal ranks of the complex component in general solution are given.Applying the conclusions obtained,the necessary and sufficient conditions for the existence of pure non-complex solutions of the equations are discussed.

关 键 词：矩阵方程组 复表示 极秩 分块矩 

分 类 号：O151.21[理学—数学]