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The \(Q_0\)-matrix completion problem. (English) Zbl 1488.15010

Summary: A matrix is a \(Q_0\)-matrix if for every \(k\in\{1,2,\dots,n\}\), the sum of all \(k\times k\) 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.

MSC:

15A12 Conditioning of matrices
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
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References:

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