Best rank one approximation of real symmetric tensors can be chosen symmetric

作     者：Shmuel FRIEDLAND 

作者机构：Department of Mathematics Statistics and Computer Science University of Illinois at ChicagoChicago IL 60607-7045 USA 

出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)

年 卷 期：2013年第8卷第1期

页      面：19-40页

核心收录：

学科分类：0810[工学-信息与通信工程] 07[理学] 08[工学] 070104[理学-应用数学] 081001[工学-通信与信息系统] 0701[理学-数学] 

基　　金：supported by the NSF 

主　　题：Symmetric tensor rank one approximation of tensors uniquenessof rank one approximation 

摘      要：We show that a best rank one approximation to a real symmetric tensor, which in principle can be nonsymmetric, can be chosen symmetric. Furthermore, a symmetric best rank one approximation to a symmetric tensor is unique if the tensor does not lie on a certain real algebraic variety.