On the Hadamard exponential GCD-matrices

In this paper we study the n n Hadamard exponential GCD matrix E[e{i,j}]n_{i,j}1 whose ij entry is e{i,j}. We give the structure theorem and calculate the determinant, the trace, inverse and determine upper bound for determinant of the Hadamard exponential GCD matrix. Furtermore determine lower bound for the Euclidean norm of the Hadamard exponential GCD matrix.