Nordström, Kenneth2017-12-152017-12-152018-02-01Kenneth Nordström, A note on the convexity of the Moore–Penrose inverse, In Linear Algebra and its Applications, Volume 538, 2018, Pages 143-14800243795https://www.sciencedirect.com/science/article/pii/S0024379517305955http://nur.nu.edu.kz/handle/123456789/2936Abstract This note is a sequel to an earlier study (Nordström [7]) on convexity properties of the inverse and Moore–Penrose inverse, in which the following question was raised. Given nonnegative definite matrices A and B with Moore–Penrose inverses A+ and B+, respectively, can one show that(λA+λ‾B)+⩽λA++λ‾B+ holding for a single λ∈]0,1[ is enough to guarantee its validity for all λ∈]0,1[? (The ordering above is the partial ordering, induced by the convex cone of nonnegative definite matrices, and λ‾:=1−λ.) In this note an affirmative answer is provided to this question.enGeneralized inverseJensen convexityLoewner orderingMidpoint convexityArticle© 2017 Elsevier Inc. All rights reserved.