On binary relation of dual core generalized inverses
Bibekananda Sitha, Dijana Mosić · Linear and Multilinear Algebra · 2025
For the dual generalized inverse, the dual index and dual core generalized inverses have just been introduced in Wang and Gao [The dual index and dual core generalized inverse. Open Math. 2023;21(1):Paper No. 20220592, 23]. The decomposition of dual core-EP generalized inverse for dual matrices has already been proposed recently in Sitha et al. [Dual core-EP generalized inverse and decomposition. Linear Multilinear Algebra. 2025. doi: 10.48550/arXiv.2502.04652]. In this study, a binary relation on dual core generalized inverse is introduced. We obtain characterizations of the dual core generalized inverses by applying the dual core-EP decomposition. A new dual binary core relation is introduced using a dual generalized core inverse. It is demonstrated that the D-core binary relation is a partial order relation, but in general, C-core relation is not a partial order.