Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8898063 | Linear Algebra and its Applications | 2018 | 6 Pages |
Abstract
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+λâ¾B)+⩽λA++λâ¾B+ holding for a single λâ]0,1[ is enough to guarantee its validity for all λâ]0,1[? (The ordering above is the partial ordering, induced by the convex cone of nonnegative definite matrices, and λâ¾:=1âλ.) In this note an affirmative answer is provided to this question.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Kenneth Nordström,