@article{bowers_evers_hogben_shaner_snider_wangsness_2006, title={On completion problems for various classes of P-matrices}, volume={413}, ISSN={["1873-1856"]}, DOI={10.1016/j.laa.2005.10.007}, abstractNote={A P -matrix is a real square matrix having every principal minor positive, and a Fischer matrix is a P -matrix that satisfies Fischer’s inequality for all principal submatrices. In this paper, all patterns of positions for n × n matrices, n ⩽ 4, are classified as to whether or not every partial Π -matrix can be completed to a Π -matrix for Π any of the classes positive P -, nonnegative P -, or Fischer matrices. Also, all symmetric patterns for 5 × 5 matrices are classified as to completion of partial Fischer matrices, and all but two such patterns are classified as to positive P - or nonnegative P -completion. We also show that any pattern whose digraph contains a minimally chordal symmetric-Hamiltonian induced subdigraph does not have Π -completion for Π any of the classes positive P -, nonnegative P -, Fischer matrices.}, number={2-3}, journal={LINEAR ALGEBRA AND ITS APPLICATIONS}, author={Bowers, J and Evers, J and Hogben, L and Shaner, S and Snider, K and Wangsness, A}, year={2006}, month={Mar}, pages={342–354} }