beta-matrices and beta-tensors

Abstract

In this manuscript we introduce the class of beta-matrices, which gives a new sufficient condition for the positivity of the determinant.

However, we show that nonnegative beta-matrices are not necessarily P-matrices. For column stochastic matrices, the property of being a beta-matrix is weaker than strict diagonal dominance. We extend beta-matrices to tensors and call them beta-tensors. Although they are not in general P-tensors, we prove that nonnegative beta-tensors of odd order are P-tensors.