Reverse order laws for the Drazin inverses

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

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

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.

Jacobson’s Lemma for Drazin Inverses

If a ring element α = 1 − ab is Drazin invertible, so is β = 1 − ba. We show that the Drazin inverse of β is expressible by a simple formula (in generalization of “Jacobson’s Lemma”) in terms of the Drazin inverse and the spectral idempotent of α. The commutation rules αa = a β and b α = β b are extended to the Drazin inverses, and the spectral idempotents of α and β are shown to be isomorphic....