The Sign Symmetric $P_{0,1}^+$-Matrix Completion Problem

TL;DR

This paper investigates the properties and classifications of sign symmetric $P_{0,1}^+$-matrix completion problems, providing classifications for small cases and comparing with other matrix completion methods.

Contribution

It offers a complete classification of sign symmetric $P_{0,1}^+$-matrix completions for small digraphs and analyzes their relation to other matrix completion problems.

Findings

Non-asymmetric incomplete digraphs lack sign symmetric $P_{0,1}^+$-completion.

Complete classification for digraphs of order up to four.

Comparison between sign symmetric $P_{0,1}^+$-completion and other matrix completions.

Abstract

We study sign symmetric $P_{0,1}^+$-matrix completion problem. It is shown that any non-asymmetric incomplete digraph lacks sign symmetric $P_{0,1}^+$-completion, digraphs of order at most four are completely classified and finally comparisons between sign symmetric $P_{0,1}^+$-completion and other matrix completions was given.