Inverse \(M\)-matrix completions of patterns omitting some diagonal positions
Let \(N= \{1,\dots, n\}\). The author investigates the following question: Which subsets \(Q\) of \(N\times N\) have the property that whenever \(a_{ij}\) for \((i,j)\in Q\) form a ``partial inverse \(M\)-matrix'' (i.e., \(a_{ij}\geq 0\) and if \(L\times L\subseteq Q\), then the inverse of \(\{a_{ij}:i, j\in L\}\) is an \(M\)-matrix), \(a_{ij}\) can be defined for \((i,j)\not\in Q\) so that the inverse of \(A= [a_{ij}]\) is an \(M\)-matrix?
scientific article; zbMATH DE number 1506786