Completely Positive Matrices, Graphs with no long odd cycles and graphs with no short odd cycles
Technion-Israel Institute of Technology
refreshments at 3:45pm
A matrix is completely positive if it can be factored as A=BB^T where B is
elementwise nonnegative. Such matrices arise in block designs and in
statistics and are related to copositive matrices. Clearly if A is
completely positive than it is doubly nonnegative, i.e. positive semidefinite
and elementwise nonnegative. This necessary condition is not sufficient.
If A is a nonnegative symmetric matrix and its comparison matrix is an
M-matrix than A is completely positive. This sufficient condition is not
necessary. In the talk I will describe qualitative conditions on the
matrices (in terms of odd cycles in the associated graphs) under which the
necessary condition is sufficient and the sufficient condition is
necessary. I will also discuss the smallest possible number of columns of
B in a factrization A=BB^T of a completely positive matrix.
Speaker's Contact Info: berman(at-sign)techunix.technion.ac.il
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