Some Results on the Hadamard Product of Tensors

In this paper, some fundamental properties of the Hadamard product of tensors are discussed. The closure of several classes of structured tensors under the Hadamard product is studied. As its important application, we present an upper bound on the spectral radius of the Hadamard product of nonnegative tensors. Moreover, we also provide some important inequalities on the spectral radius of the Hadamard products of the Hadamard powers for nonnegative tensors. Some numerical examples are reported to verify the effectiveness of our theoretical results.