Computer Science, Mathematics
Journal or Book Title
Linear Algebra and its Applications
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.
This manuscript version is made available under the CCBY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Bowers, John; Evers, Job; Hogben, Leslie; Shaner, Steve; Snider, Karyn; and Wangsness, Amy, "On completion problems for various classes of P-matrices" (2006). Mathematics Publications. 79.