The Q0-matrix completion problem. Issue 1 (31st July 2020)

• Record Type: Journal Article
• Authors: Sinha, Kalyan
• Is Part Of: Arab journal of mathematical sciences. Volume 27:Issue 1(2021)
• Page Start: 119
• Page End: 128
• Publication Date: 2020-07-31
• Subjects: Partial matrix -- Matrix completion -- Q0-matrix -- Q0-completion -- Digraph; MSC: 15A18
• DOI: 10.1016/j.ajmsc.2019.08.001
• Languages: English
• ISSNs: 1319-5166

Abstract

Abstract : A matrix is a Q 0 -matrix if for every k ∈ { 1, 2, …, n }, the sum of all k × k principal minors is nonnegative. In this paper, we study some necessary and sufficient conditions for a digraph to have Q 0 -completion. Later on we discuss the relationship between Q and Q 0 -matrix completion problem. Finally, a classification of the digraphs of order up to four is done based on Q 0 -completion.