Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations
Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations
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DOI：
10.1016/j.camwa.2005.01.014
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发表时间：
2005-04-01
影响因子：
2.9
通讯作者：
Wang, QW
中科院分区：
文献类型：
--
作者：
Wang, QW
本文考虑了真实的四元数代数H上某些矩阵方程的双对称和中心对称解。本文给出了矩阵方程AX = C及下列方程组A1 X = C-1，A（1）x = C-1，XB 3 = C-3，A（2）X = C-2有双对称解的充要条件，以及方程组A（1）X = C-1，A（3）XB（3）= C-3有中心对称解的充要条件.文中还给出了上述矩阵和系统的解的表达式。此外，还建立了四元数矩阵是双对称矩阵的一个判别准则，并给出了H上其它集合的一些辅助结果。(c)2005爱思唯尔有限公司保留所有权利。
In this paper we consider bisymmetric and centrosymmetric solutions to certain matrix equations over the real quaternion algebra H. Necessary and sufficient conditions are obtained for the matrix equation AX = C and the following systemsA1X = C-1, A(1)x = C-1,XB3 = C-3, A(2)X = C-2,to have bisymmetric solutions, and the systemA(1)X = C-1,A(3)XB(3) = C-3,to have centrosymmetric solutions. The expressions of such solutions of the matrix and the systems mentioned above are also given. Moreover a criterion for a quaternion matrix to be bisymmetric is established and some auxiliary results on other sets over H are also mentioned. (c) 2005 Elsevier Ltd. All rights reserved.