Consistency for bi(skew)symmetric solutions to systems of generalized Sylvester equations over a finite central algebra

By Qingwen Wang, Jiankun Sun, Shangshuai Li. 2002

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The general coupled matrix equations over generalized bisymmetric matrices (2010, background): “In [26], the authors presented the necessary and sufficient conditions for the existence of constant solutions with bi(skew)symmetric constrains to the matrix equations AiX − YBi = Ci, i = 1, 2, .”
A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity (2004, unknown): “[10–31]).”
Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations (2005, unknown): “By [19], we have the following definition.”
Computational Methods for Linear Matrix Equations (2016, background): “Necessary and sufficient conditions for the resulting systems to have a solution pair are studied in [273].”
The η-bihermitian solution to a system of real quaternion matrix equations (2014, background): “1 [3] Let A = (ai j ) ∈ Hm×n , A(∗) = (ām− j+1,n−i+1) ∈ Hn×m , A = (am−i+1,n− j+1) ∈ Hm×n , where ā j i is the conjugate of the quaternion a ji .”
On solutions to the quaternion matrix equation AXB+CYD=E (2008, unknown): “which is widely studied (see, e.g., [4], [5], [7], [8], [11], [13], [ 22 ]-[24], [33], [34]).”