两个新的张量特征值包含区域

Two New Eigenvalue Inclusion Sets for Tensors

摘要: 张量是矩阵的高阶推广，在数据分析、信号与图像处理等许多科学领域中都有重要应用，而张量的特征值是张量理论和应用研究的一个重要方面。本文给出了两个新的张量特征值包含集，证明了所得的包含集含于经典的Gersgorin特征值包含集中，并由其得到偶数阶实对称张量(半)正定性的两个充分条件。

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.