Ranks and the least-norm of the general solution to a system of quaternion matrix equations
Ranks and the least-norm of the general solution to a system of quaternion matrix equations
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四元数矩阵方程组通解的秩和最小范数
DOI：
10.1016/j.laa.2008.05.031
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发表时间：
2009-03-01
影响因子：
1.1
通讯作者：
Li, Cheng-Kun
中科院分区：
文献类型：
--
作者：
Wang, Qing-Wen;Li, Cheng-Kun
本文首先建立了最近研究的相容线性四元数矩阵方程组A（1）X（1）= C-1，A（2）X（2）= C-2，A（3）X（1）B（1）+ A（4）X（2）B（2）= C-3的通解的一个新表达式.王惠熙张昌义<英>香港实业家。林，四元数矩阵方程组的P-（斜）对称公共解，应用数学计算。195（2008）721-732]，然后导出上述系统的通解的最大和最小秩以及最小范数。一些已知的结果可以看作是本文结果的特例。(c)2008年爱思唯尔公司All rights reserved.
We in this paper first establish a new expression of the general solution to the consistent system of linear quaternion matrix equations A(1)X(1) = C-1, A(2)X(2) = C-2, A(3)X(1)B(1) + A(4)X(2)B(2) = C-3, which was investigated recently [Q.W. Wang, H.X. Chang, C.Y. Lin, P-(skew) symmetric common solutions to a pair or quaternion matrix equations, Appl. Math. Comput. 195 (2008) 721-732], then derive the maximal and minimal ranks and the least-norm of the general solution to the system mentioned above. Some previous known results can be viewed as special cases of the results of this paper. (c) 2008 Elsevier Inc. All rights reserved.