Consimilarity of quaternion matrices and complex matrices

This paper discusses consimilarity of quaternion matrices, obtains the Jordan canonical form of a quaternion matrix under consimilarity, and some necessary and sufficient conditions for consimilarity of quaternion matrices. The consimilarity of quaternion matrices is a natural extension of the complex consimilarity of complex matrices, has many good properties including some that are essentially different from those of complex consimilarity. Moreover, using the consimilarity of quaternion matrices, we obtain a new way to discuss complex consimilarity of complex matrices.