Consimilarity of quaternion matrices and complex matrices

This paper discusses consimilarity of quaternion matrices, obtains the Jord an canonical form of a quaternion matrix under consimilarity, and some nece ssary and sufficient conditions for consimilarity of quaternion matrices. T he consimilarity of quaternion matrices is a natural extension of the compl ex consimilarity of complex matrices, has many good properties including so me that are essentially different from those of complex consimilarity. More over, using the consimilarity of quaternion matrices, we obtain a new way to discuss complex consimilarity of complex matrices. (C) 2001 Elsevier Sci ence Inc. All rights reserved.