Dual r -rank decomposition and its applications

In this paper, we introduce the dual r -rank decomposition of the dual matrix, get its existence conditions and equivalent forms of the decomposition. Then we derive some characteristics 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 composition, we derive several characteristics of the dual EP matrix, dual annotated matrix, dual generalized inverses, and relationships among dual Penrose equations.