The Determinations And Properties Of H Tensor

Tensor is an important branch discipline of mathematics,and a high-order extension of matrices.It is also a multi-linear function that can be used to represent vector and scalar linear relationships.In recent years,tensor theory has been used in digital signal processing,data analysis and data mining,medicine problems such as image scanning and processing,nonlinear optimization problems,quantum entanglement problems,chemical dose usage problems,psychological tests and other aspects in our life.With the development of tensor theory,many new problems are worth exploring,leading us to explore the theoretical value and practical significance of tensor.The non-singular H tensor is an indispensable part of the tensor theory and plays an important role in solving life problems.The method of studying the eigenvalues of non-singular H tensor can be used to determine its positive definiteness.However,the theoretical analysis of this method is too complicated and the computational complexity is very difficult,so it is not an ideal determination method.The scholars proposed an iterative algorithm for determining non-singular H tensor after research and promotes the development of non-singular H tensor theory.Due to the relationship between non-singular H tensor and positive definite tensors,scholars have paid much more attention to research non-singular H tensor in recent years.There are many difficulties in research when scholars researching the determination of non-singular H tensors,especially large-scale non-singular H tensor.Therefore,it is very necessary to study the determination theory of non-singular H tensor.On the basis of relevant studies,this article has conducted an in-depth study of the determination and properties of non-singular H tensor.Based on the generalized strict diagonal dominant of tensors and the existing determination rules of non-singular H tensor,researched and created some conditions to reconstruct the criteria for the determination of non-singular H tensor for general tensors and irreducible tensors,and at last,using numerical examples to illustrate the validity of the criteria.