Abstract
An n × n real matrix is said to be totally nonpositive if every minor is nonpositive. In this paper, we are interested in totally nonpositive completion problems, that is, does a partial totally nonpositive matrix have a totally nonpositive matrix completion? This problem has, in general, a negative answer. Therefore, we analyze the question: for which labeled graphs G does every partial totally nonpositive matrix, whose associated graph is G, have a totally nonpositive completion? Here we study the mentioned problem when G is a chordal graph or an undirected cycle. © 2005 Elsevier Inc. All rights reserved.
Keywords
Partial matrix Completion problem Totally nonpositive matrix Undirected graphs
Referencia
C.M. Araújo, J.R. Torregrosa, A.M. Urbano (2005): Totally nonpositive completions on partial matrices. Linear Algebra and its Applications 413 (2006) 403–424.
