Some results on B-matrices and doubly B-matrices

Abstract

A real matrix with positive row sums and all its off-diagonal elements bounded above by their corresponding row means was called in [4] a B-matrix. In [5], the class of doubly B-matrices was introduced as a generalization of the previous class. We present several characterizations and properties of these matrices and for the class of B-matrices we consider corresponding questions for subdirect sums of two matrices (a general ‘sum’ of matrices introduced in [1] by S.M. Fallat and C.R. Johnson, of which the direct sum and ordinary sum are special cases), for the Hadamard product of two matrices and for the Kronecker product and sum of two matrices.