# 两个新的张量特征值包含区域Two New Eigenvalue Inclusion Sets for Tensors

Abstract: The concept of tensors is a generalization of matrices to high order. And there are some important applications in many scientific fields, such as data analysis, signal and image processing and so on. Tensor eigenvalue theory is an important aspect of tensor research and application. In this paper, two new eigenvalue inclusion sets for tensors are given, and it is proved that the new eigenvalue inclusion sets are tighter than the classical Gersgorin inclusion set. In addition, as applications of the results, two sufficient conditions for the (semi-)positive definite property of the even order symmetric tensors are obtained.

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