The New Eigenvalue Inclusion Sets For Tensor

The concept of tensors is a generalization of matrices to high order. And there are some important applications in many scientific fields, such as signal and image processing, data analysis and so on. Tensor eigenvalue theory is an important aspect of tensor research. In this thesis, the eigenvalue inclusion sets for tensor are researched, and three new eigenvalue inclusion sets for tensor are given. In addition, it is proved that the new eigenvalue inclusion sets are tighter than the classical Gerschgorin inclusion set. Furthermore, two new eigenvalue inclusion sets are contained in the literature [Chaoqian Li, Zhen Chen, Yaotang Li. A new eigenvalue inclusion set for tensors and its applications, Linear Algebra Appl. (2015) 481-53.36].