Simultaneously reducing two quaternionic matrices and its applications (Q1011895)

Given two \(m\times n\) quaternionic matrices \(A\) and \(B\), the author proves that \(A\) and \(B\) can be equivalent to complex matrices simultaneously. As applications, he converts some quaternionic matrix equations into the equivalent complex counterparts, thereby obtains an approach of determining the consistency and finding the general solutions of them without any additional assumption.