Determinantal representations of solutions to systems of two-sided quaternion matrix equations
Ivan Kyrchei · Linear and Multilinear Algebra · 2019
Within the framework of the theory of quaternion row-column determinants previously introduced by the author, we derive determinantal representations (analogs of Cramer's rule) of a solution to the system of two-sided quaternion matrix equations A1XB1=C1, A2XB2=C2 and its special cases with one one-sided equation when B1=I or A1=I, where I is an identity matrix of appropriate shape. Since the Moore–Penrose inverse is a necessary tool to solve matrix equations, we use determinantal representations of the Moore–Penrose inverse previously obtained by the theory of row-column determinants as well.