Reverse order laws for Hirano inverses in rings

Reverse order laws for {1, 2, 3}-generalized inverses

In this paper, we present purely algebraic necessary and sufficient conditions for reverse order laws for {1, 2, 3} and {1, 2, 4}-generalized inverses on the set of matrices. 2010Mathematics Subject Classification: 15A09

Reverse order laws for the weighted generalized inverses

In this paper, we offer new necessary and sufficient conditions for the reverse order laws to hold for the weighted generalized inverses of matrices. 2010 Mathematics Subject Classification: 15A09

The reverse order laws and the mixed-type reverse order laws for generalized inverses of multiple matrix products

Ela the Reverse Order Laws and the Mixed-type Reverse Order Laws for Generalized Inverses of Multiple Matrix Products

In this paper, necessary and sufficient conditions for a number of reverse order laws and mixed-type reverse order laws are derived by using the maximal ranks of the generalized Schur complements.

The absorption laws for the generalized inverses in rings

In this paper, it is given equivalent conditions for the absorption laws in terms of the Moore-Penrose, group, core inverse, core inverse dual, {1}, {1,2}, {1,3}, and {1,4} inverses in rings. The results given here extend the results of [X. Liu, H. Jin, and D.S. Cvetković-Ilić. The absorption laws for the generalized inverses. Appl. Math. Comp., 219:2053–2059, 2012.].