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.