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+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.
Original language | English |
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Pages (from-to) | 143-148 |
Number of pages | 6 |
Journal | Linear Algebra and Its Applications |
Volume | 538 |
DOIs | |
Publication status | Published - Feb 1 2018 |
Keywords
- Generalized inverse
- Jensen convexity
- Loewner ordering
- Midpoint convexity
ASJC Scopus subject areas
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics