Brualdi-type Inequalities on Spectral Radius for the Hadamard Product of Nonnegative Tensors

In this paper, we use the theories of directed graph and diagonally similar transformation to give some new inequalities called Brualdi-type inequalities on spectral radius for the Hadamard product of nonnegative tensors, which improve some existing ones in [Linear Multilinear Algebra, 2018, 66(6): 1199–1214] and [Bull. Iranian Math. Soc., 2020, 46(4): 1003–1026]. Furthermore, we also establish the theoretical comparison between the newly proposed bounds under certain conditions. Finally, the validity and the sharpness of the main results are illustrated by some numerical examples.