| In 2005,Professor L.Q.Qi coming from Hong Kong Polytechnic University and Professor L.H.Lim working in the University of Chicago proposed the concepts of eigenvalues of tensors,respectively.Since then,it has been paid closed attention in academic area and this also attracted worldwide scholars to participate in the research on properties of tensor eigenvalues,such as nonnegative tensor theory and hypergraph theory and so on.In 2010,K.C.Chang et al.gave the concepts of rectangular tensor and singular value of rectangular tensor,respectively.In 2013,K.C.Chang et al.gave the definition of tensor z-eigenvalue.In 2013,C.Ling et al.gave a more general definition of the singular values of rectangular tensors,that is,the lk,s singulaF values of rectangular tensors.Singular values of rectangular tensors and z-eigenvalues are widely used,such as medical resonance imaging,data analysis,high-order Markov chains,and judging the positive definiteness of even-order multivariate forms in the theory of control.In this thesis,the inclusion sets of z-eigenvalues of tensors,Brualdi-type inclusion sets of singular values of rectangular tensors,inclusion sets of C-eigenvalues of piezoelectric tensors and inclusion sets of M-eigenvalues of elastic tensors are given.This thesis generalizes the theorem about Brualdi-type inclusion sets of eigenvalues of matrix and obtain the theorem about Brualdi-type inclusion sets of z-eigenvalues of tensors.Compared with the previous inclusion sets of z-eigenvalues of tensors,it is proved that the bound of the inclusion sets of z-eigenvalues of tensors in this paper are smaller than[71].Brualdi-type inclusion sets for lk,s singular values of rectangular tensors are given.The inclusion sets of C-eigenvalues of piezoelectric tensors and M-eigenvalues of elasticity tensors are given,and the ranges of C-eigenvalues of eight piezoelectric tensors and M-eigenvalues of two elastic tensors in practical applications are given. |
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