On completion problems for various classes of \(P\)-matrices
A \(P\)-matrix is a real square matrix having every principal minor positive; a Fischer matrix is a \(P\)-matrix satisfying Fischer's inequality for all principal submatrices, i.e., \(\det A[\alpha] \det A[\beta] \geq \det A[\alpha \cup \beta]\) where \(\alpha, \beta \in 2^{\{1, ..., n\}}\) with \(\alpha \cap \beta = \emptyset\). The authors classify all patterns of positions for \((n \times n)\)-matrices, \(n \leq 4\), as to whether or not every partial positive \(P\)-matrix (non-negative \(P\)-matrix, Fischer matrix, respectively) can be completed to a matrix of the respective class.
scientific article; zbMATH DE number 5014288