Abstract
An n×n matrix over the field of real numbers is a doubly negative matrix if it is symmetric, negative definite and entry-wise negative. In this paper, we are interested in the doubly negative matrix completion problem, that is when does a partial matrix have a doubly negative matrix completion. In general, we cannot guarantee the existence of such a completion. In this paper, we prove that every partial doubly negative matrix whose associated graph is a pchordal graph G has a doubly negative matrix completion if and only if p = 1. Furthermore, the question of completability of partial doubly negative matrices whose associated graphs are cycles is addressed. © 2004 Elsevier Inc. All rights reserved.
Keywords
Matrix completion problem DN-matrix Undirected graphs
Referencia
C.M. Araújo, J.R. Torregrosa, A.M. Urbano (2004): The doubly negative matrix completion problem. Linear Algebra and its Applications 401 (2005) 295–306.
