NOTES ON COMPLETELY POSITIVE MATRICES

Let A be a n X n symmetric matrix and in the closure of inverse M-matr ices. Then A can be factored as A = BBT for some nonnegative lower tri angular n X n matrix B, and cp-rank A less than or equal to n. If A is a positive semidefinite (0, 1) matrix, then A is completely positive and cp-rank A = rank A; if A is a nonnegative symmetric H-matrix, then A is completely positive and cp-rank A less than or equal to n(n + 1) /2 - N - (n - mu), where mu, is the number of connected components of the graph G(A). (C) 1998 Elsevier Science Inc.