  In this paper, we introduce the dual $r$-rank decomposition of dual matrix,
get its existence condition and equivalent form of the decomposition, as well
as derive some characterizations of dual Moore-Penrose generalized
inverse(DMPGI). Based on DMPGI, we introduce one special dual matrix(dual EP
matrix). By applying the dual $r$-rank decomposition we derive several
characterizations of dual EP matrix, dual idempotent matrix, dual generalized
inverses, and the relationships among dual Penrose equations.
