479,097 research outputs found
Factorization of CP-rank-3 completely positive matrices
A symmetric positive semi-definite matrix A is called completely positive if
there exists a matrix B with nonnegative entries such that A=BB^T. If B is such
a matrix with a minimal number p of columns, then p is called the cp-rank of A.
In this paper we develop a finite and exact algorithm to factorize any matrix A
of cp-rank 3. Failure of this algorithm implies that A does not have cp-rank 3.
Our motivation stems from the question if there exist three nonnegative
polynomials of degree at most four that vanish at the boundary of an interval
and are orthonormal with respect to a certain inner product.Comment: 13 pages, 10 figure
The Roots and Links in a Class of -Matrices
In this paper, we discuss exiting roots of sub-kernel transient matrices
associated with a class of matrices which are related to generalized
ultrametric matrices. Then the results are used to describe completely all
links of the class of matrices in terms of structure of the supporting tree.Comment: 11 pages, 1 figur
- β¦