Semi-central Bott–Duffin $(e,f)$-inverses - Fang, Li; Zhao, Liang; Fang, Li; Zhao, Liang (Institute of Mathematics, NAS of Ukraine, 2026)
UDC 512.552 We study Bott–Duffin $(e,f)$-inverses in the context of left and right semi-central idempotents. A new class of generalized inverses named semi-central Bott–Duffin $(e,f)$-inverses is introduced and studied.  An example is given to show that the Bott–Duffin $(e,f)$-inverses are not necessarily semi-central Bott–Duffin $(e,f)$-inverses. It is shown that the semi-central Bott–Duffin $(e,f)$-inverses exhibit additional properties beyond the properties of general Bott–Duffin $(e,f)$-inverses. As applications, we examine semi-central Bott–Duffin $(e,f)$-inverses for several classes of matrices.