Sufficient conditions for complete positivity
Robert Reams · Operators and Matrices · 2011
Marcus and Minc gave sufficient conditions on the diagonal entries of a doubly nonnegative doubly stochastic n n matrix A , that there is a doubly nonnegative doubly stochastic matrix C with A = C 2 . In this event, A is completely positive. We shall assume that A is doubly nonnegative and irreducible and provide slightly more general sufficent conditions on the diagonal entries of A for the existence of C . Our main result provides sufficient conditions on the principal 2 2 minors of a doubly nonnegative doubly stochastic irreducible matrix A for the existence of C .