ELA, Volume 10, pp. 257-271, November 2003, abstract.
The (Weakly) Sign Symmetric P-matrix Completion Problems
Luz Maria DeAlba, Timothy L. Hardy, Leslie Hogben and
Amy Wangsness
In this paper it is shown that a partial sign symmetric
P-matrix, whose digraph of specified entries is a symmetric
n-cycle with n greater than or equal to 6, can be completed
to a sign symmetric P-matrix. The analogous completion
property is also established for a partial weakly sign
symmetric P-matrix and for a partial weakly sign symmetric
P_0-matrix. Patterns of entries for 4-by-4 matrices are
classified as to whether or not a partial (weakly) sign
symmetric P- or weakly sign symmetric P_0-matrix specifying
the pattern must have completion to the same type of matrix.
The relationship between the weakly sign symmetric P- and
sign symmetric P-matrix completion problems is also examined.