The P_0,1⁺-matrix completion problem

Abstract

In this paper, the P_0,1⁺-matrix completion is introduced. A real n × n matrix is a P_0,1⁺-matrix if it is a P₀⁺-matrix with all positive diagonal entries. Firstly some necessary conditions for P_0,1⁺-matrix completion are obtained and later on some sufficient conditions are also shown. Also the relationship between the P_0,1⁺-matrix completion problem and other completion problems of p-matrix classes are discussed. Finally most of the digraphs of order at most 4 having P_0,1⁺-completion are classified.

Keywords:

• Partial matrix
• Matrix completion
• Digraph
• P_0,1⁺-matrix
• P_0,1⁺-completion

Mathematics Subject Classification:

• 15A48