On the Centro-symmetric Solution of a System of Matrix Equations over a Regular Ring with Identity
On the Centro-symmetric Solution of a System of Matrix Equations over a Regular Ring with Identity
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DOI：
10.1142/s100538670700051x
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发表时间：
2007-12
影响因子：
0.3
通讯作者：
Qingwen Wang;Haixia Chang;Chun-Yan Lin
中科院分区：
文献类型：
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作者：
Qingwen Wang;Haixia Chang;Chun-Yan Lin
本文求出了任意正则环上矩阵方程组的中心对称解。我们首先给出了矩阵方程组A1X1=C1，A2X1=C2，A3X2=C3，A4X2=C4和A5X1B5+A6X2B6=C5存在的充要条件和通解的显式表达式。利用上述结果，我们建立了环上矩阵方程组AAX=Ca，ABX=Cb和AcXBc=Cc的一般中心对称解的存在性和表示的两个判据。
In this paper, we find the centro-symmetric solution of a system of matrix equations over an arbitrary regular ring with identity. We first derive some necessary and sufficient conditions for the existence and an explicit expression of the general solution of the system of matrix equations A1X1 = C1, A2X1 = C2, A3X2 = C3, A4X2 = C4 and A5X1B5 + A6X2B6 = C5 over . By using the above results, we establish two criteria for the existence and the representation of the general centro-symmetric solution of the system of matrix equations AaX = Ca, AbX = Cb and AcXBc = Cc over the ring .