On a class of nonsingular matrices containing 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 [12] a B-matrix. The classes of doubly B-matrices and of $B^R_{\pi}$-matrices were introduced in [13] and [11] as generalizations of the previous class. We present characterizations and properties of $B^R_{\pi}$-–matrices and we consider the problem of when a subdirect sum of two matrices in this class lies in the same class.