Some inequalities for the Hadamard product of tensors

Let A = (a_i1···im) and B = (b_i1···im) be two order m dimension n tensors. The Hadamard product A ◦ B is an order m dimension n tensor with entries (A ◦ B)_i1···im = ai_1···b_i1···im. For nonnegative tensors A and B, we obtain some bounds on spectral radius of A ◦ B in terms of spectral radius and entries of A and B. We give some inequalities for the minimum eigenvalue and determinant of the Hadamard product involving M-tensors and Z-tensors, and use them to derive some criteria of M-tensors.