The maximal cp-rank of rank k completely positive matrices Original Research Article

Let Φk be the maximal cp-rank of all rank k completely positive matrices. We prove that Φk=k(k+1)/2−1 for kgreater-or-equal, slanted2. In particular we furnish a procedure to produce, for kgreater-or-equal, slanted2, completely positive matrices with rank k and cp-rank k(k+1)/2−1.