Hadamard Products Of Tensors With Applications

Hadamard product of matrices is an important concept in matrix theory, it is a special multiplication of matrices, and has important applications in many fields. In this thesis, the concept of Hadamard products of matrices is extended to the higher order tensors, some basic properties of Hadamard products of tensors are discussed, Hadamard products of several structural tensors are studied, and an estimate formulas of the upper bound on the spectral radius of Hadamard product of non-negative tensors is given by using the properties of Hadamad products of tensors. The numerical example shows that the estimate formula could be used to estimate the upper bound of the spectral radius for non-negative tensors.