 
Summary: Mathematics
and
Statistics
COLLOQUIUM
Shahla Nasserasr
University of Regina
Conditions for a
TP2Completion
Friday, February 11, 2011
3:30 p.m.
Mathematics and Statistics Lounge, CW 307.20
Abstract: A matrix is called TP2 if all 1by1 and 2by2 minors are positive.
A TP2completion of a partial TP2 matrix T, is a choice of values for the un
specified entries of T so that the resulting matrix is TP2. The TP2completion
problem asks which partial matrices have a TP2completion. The Bruhat order on
permutations and the notion of majorization are generalized to partial orders on
nonnegative matrices. Using these partial orders and the Hadamard exponential
transformation, explicit conditions for TP2completability of a given partial ma
trix are given. The theory of cones and generators, and the logarithmic method
are used to reduce these conditions to a set of minimal conditions. It turns out
