Abstract
Let S be a subset of the set of real numbers R. A is called S- factorizable if it can be factorized as A= BB T with b ij ∈ S. The smallest possible number of columns of B in such factorization is called the S-rank of A and is denoted by rank S A. If S is a set of nonnegative numbers, then A is called S- cp. The aim of this work is to study {0,1}- cp matrices. We characterize {0,1}- cp matrices of order less than 4, and give a necessary and sufficient condition for a matrix of order 4 with some zero entries, to be {0,1}- cp. We show that a nonnegative integral Jacobi matrix is {0,1}- cp if and only if it is diagonally dominant, and obtain a necessary condition for a 2-banded symmetric nonnegative integral matrix to be {0,1}- cp. We give formulae for the exact value of the {0,1}-rank of integral symmetric nonnegative diagonally dominant matrices and some other {0,1}- cp matrices.
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