Combined matrices in special classes of matrices

AbstractThe combined matrix of a nonsingular matrix A is the matrix A∘(A-1)T, where ∘ means the Hadamard (entrywise) product. It has simple properties, its row- as well as column-sums are always one, and it is not changed if A is multiplied from either side by a nonsingular diagonal matrix. Although it is usually difficult to compute, its further properties deserve attention. In the paper, we concentrate on the sequence of the diagonal entries of combined matrices in various classes of matrices