Essentially Positive Rectangular Tensors And Eigenvalues Of Nonnegative Tensors

Higher order tensors are higher order generalizations of the matrice. The eigenvalue problems of higher-order tensors have become an important topic of study in a new ap-plied mathematics branch, numerical multilinear algebra. The real rectangular tensors arise from the strong ellipticity condition problem in solid mechanics and the entangle-ment problem in quantum physics. In this paper, we systematically study definitions and properties of essentially positive rectangular tensors, weakly positive rectangular tensors and give some conclusions on the eigenvalue of some classes of nonnegative square tensors. The full text is divided into four parts.In the first part, we briefly introduce the research background and current situation of the tensor, and probe into the main content of the paper.In the second part, we recall the basic concepts of tensors.In the third part, we study definitions and properties of essentially positive rect-angular tensors and weakly positive rectangular tensors.In the fourth part, we mainly investigate some properties about some classes of nonnegative square tensors.