Abstract
This paper carries further the study of core partial order initiated by Baksalary
and Trenkler [Core inverse of matrices, Linear Multilinear Algebra. 2010;58:
681697]. We have extensively studied the core partial order, and some new
characterizations are obtained in this paper. In addition, simple expressions for
the already known characterizations of the minus, the star (and one-sided star),
the sharp (and one-sided sharp) and the diamond partial orders are also obtained
by using a HartwigSpindelb¿ock decomposition.