On the Centro-symmetric Solution of a System of Matrix Equations over a Regular Ring with Identity
Qing‐Wen Wang, Haixia Chang, Chunyan Lin · Algebra Colloquium · 2007
In this paper, we find the centro-symmetric solution of a system of matrix equations over an arbitrary regular ring [Formula: see text] 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 [Formula: see text]. 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 [Formula: see text].