On solutions to the quaternion matrix equation AXB+CYD=E
On solutions to the quaternion matrix equation AXB+CYD=E
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DOI：
10.13001/1081-3810.1268
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发表时间：
2008
影响因子：
0.7
通讯作者：
Qingwen Wang;Huasheng Zhang;Shao-Wen Yu
中科院分区：
文献类型：
--
作者：
Qingwen Wang;Huasheng Zhang;Shao-Wen Yu
给出了一致四元数矩阵方程AXB+CY D = e的实解和纯虚解存在的表达式和充分必要条件。建立了实矩阵Xi、Yi、i =1、···、4在解对X = X1 +X2i +X3j +X4k和Y = Y1 +Y2i +Y3j +Y4k中的极值秩的表达式。并给出了该方程所有解对X和Y分别为实或纯虚的充分必要条件。一些已知的结果可以看作是本文结果的特例。
Expressions, as well as necessary and sufficient conditions are given for the existence of the real and pure imaginary solutions to the consistent quaternion matrix equation AXB+CY D = E. Formulas are established for the extreme ranks of real matrices Xi,Yi,i =1 ,···, 4, in a solution pair X = X1 +X2i +X3j +X4k and Y = Y1 +Y2i +Y3j +Y4k to this equation. Moreover, necessary and sufficient conditions are derived for all solution pairs X and Y of this equation to be real or pure imaginary, respectively. Some known results can be regarded as special cases of the results in this paper.