The non-negative $Q_1$-matrix completion problem
Authors :
Kalyan Sinha
Author Address :
Department of Mathematics, A. B. N. Seal College, Coochbehar, India-736101.
Abstract :
A matrix is a $Q_1$-matrix if it is a $Q$-matrix with positive diagonal entries. A matrix is a nonnegative matrix if it is a matrix with nonnegative entries. A digraph $D$ is said to have nonnegative $Q_1$-completion if every partial nonnegative $Q_1$-matrix specifying $D$ can be completed to a nonnegative $Q_1$-matrix. In this paper, some necessary and sufficient conditions for a digraph to have nonnegative $Q_1$-completion are provided. Later on the relationship among the completion problems of nonnegative $Q_1$-matrix and some other class of matrices are shown. Finally, the digraphs of order at most four that include all loops and have nonnegative $Q_1$-completion are singled out.
Keywords :
Partial matrix, Nonnegative $Q_1$-matrix, Digraph, Matrix completion, Nonnegative $Q_1$-completion problem.
DOI :
Article Info :
Received : April 12, 2019; Accepted : August 08, 2019.
