New Eigenvalue Inclusion Sets For Tensors

The concept of tensors is a generalization of matrices to high order.Tensor theory has been widely used in many aspects,such as medical magnetic resonance imaging,high order Markov chain and so on.The eigenvalue problem of tensors is one of the important aspects in the study of tensor theory and its applications.In this thesis,we study the localization of tensor eigenvalues,and obtain three new eigenvalues inclusion sets of tensors.It is proved that the new eigenvalue inclusion sets are tighter than the classical Gersgorin inclusion set,and one of them is contained in the eigenvalue inclusion set for tensors which is in the paper[C.Q.Li,Z.C,Y.T.Li,A new eigenvalue inclusion set for tensors and its applications,Linear Algebra and its Application,2015(481):36-53.].Finally,a sufficient condition for the positive definite of an even order real symmetric tensor and a new eigenvalues inclusion set of a matrix are given by using the eigenvalue inclusion sets of tensors.