The maximal cp-rank of rank k completely positive matrices

Let <f>Φk</f> be the maximal cp-rank of all rank k completely positive matrices. We prove that <f>Φk=k(k+1)/2−1</f> for <f>k&ges;2</f>. In particular we furnish a procedure to produce, for <f>k&ges;2</f>, completely positive matrices with rank k and cp-rank <f>k(k+1)/2−1</f>. [Copyright &y& Elsevier]