A note on the convexity of the Moore–Penrose inverse

Kenneth Nordstrom Olof

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)143-148
Number of pages6
JournalLinear Algebra and Its Applications
Volume538
DOIs
Publication statusPublished - Feb 1 2018

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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

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