Completely Positive Realizations of a Cycle

Abstract:

      An n × n real matrix A is called doubly nounegative, if A is entrywise nonnegative and semidefmite positive as well. A is called completely positive if A can be factored as A=BB^t,where B is some nonnegative n × m matrix. The smallest such number m is called the factorization index (or CP-rank) of A. This paper presents a criteria for a doubly nonnegative matrix realization of a cycle to be completely positive, which is strightforward and effective.