The non-negative $Q_1$-matrix completion problem
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DOI:
https://doi.org/10.26637/MJM0704/0007Abstract
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 Q1-matrix, Digraph, Matrix completion, Nonnegative Q1-completion problem.Mathematics Subject Classification:
Mathematics- Pages: 651-658
- Date Published: 01-10-2019
- Vol. 7 No. 04 (2019): Malaya Journal of Matematik (MJM)
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