We give a formula of(P+Q)Dunder the conditionsP2Q+QPQ=0,P3Q=0, andPQPQ=0. Then, we apply it to give some expressions for the Drazin inverse of block matrixM=(ABCD)(AandDare square matrices) under some conditions, generalizing some recent results in the literature. Finally, numerical examples are given to illustrate our results.
Abstract. This article aims to present some unitarily invariant norms inequalities involving Heron and Heinz means for matrices. We give some refinements for the results presented by R. Kaur and M. Singh in [Math. Ineq. Appl., 16 (2013) 93-99].Mathematics subject classification (2010): 47A30, 15A60.
Abstract. In this paper, we give a formula of (P + Q) D under the conditions P 2 Q + QP Q = 0 and P 3 Q = 0. Then applying it to give some results) (A and D are square matrices) with generalized Schur complement is zero under some conditions. Finally, numerical examples are given to illustrate our results.
This paper aims to present some operator inequalities for positive linear maps. These inequalities are refinements of the results presented by Xue in [
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.