We prove that a CP matrix A having cyclic graph has exactly two minimal rank 1 factorization if det M(A) > 0 and has exactly one minimal rank 1 factorization if detM(A) = 0.
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=BBt,where B is some nonnegative n ...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=BBt,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.展开更多
文摘We prove that a CP matrix A having cyclic graph has exactly two minimal rank 1 factorization if det M(A) > 0 and has exactly one minimal rank 1 factorization if detM(A) = 0.
基金Supported by Anhui Edncation Committee(LJ990007)
文摘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=BBt,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.
