ELA, Volume1, pp. 59-63, November 1996, abstract.

The Combinatorially Symmetric P-matrix Completion Problem

Charles R. Johnson and Brenda K. Kroschel

An n-by-n real matrix is called a P-matrix if all its principal 
minors are positive. The P-matrix completion problem asks which 
partial P-matrices have a completion to a P-matrix. Here, we prove 
that every partial P-matrix with combinatorially symmetric specified 
entries has a P-matrix completion. The general case, in which the 
combinatorial symmetry assumption is relaxed, is also discussed.