The reverse order law for the generalized Bott-Duffin inverses of matrices
CAO Zhiqiang, Nailin Du · DOAJ (DOAJ: Directory of Open Access Journals) · 2019
In this paper we investigate the reverse order law for the generalized Bott-Duffin inverses of two L-p.s.d.matrices.The concept of L-p.s.d.matrices is a generalization of semi-positive definiteness,in the sense that Rn-p.s.d.matrices are exactly semi-positive definite matrices.We establish a relationship between generalized Bott-Duffin inverses and AS,S⊥(2) inverses,and by using their properties,give necessary and sufficient conditions for the reverse order law of the generalized Bott-Duffin inverses.In the end we give two explicit examples to test our results.