Nonnegative Combined Matrices

Abstract

The combined matrix of a nonsingular real matrix $A$ is the Hadamard (entrywise) product $A\circ {\left(A^{-1}\right)}^T$. It is well known that row (column) sums of combined matrices are constant and equal to one. Recently, some results on combined matrices of different classes of matrices have been done. In this work, we study some classes of matrices such that their combined matrices are nonnegative and obtain the relation with the sign pattern of $A$. In this case the combined matrix is doubly stochastic.