Numerical ranges of tensors

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• 作者：Rihuan Ke^a ; ¹ ; ^{krhuan@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Wen Li^a ; ² ; ^{liwen@scnu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Michael K. Ng^b ; ³ ; ^{mng@math.hkbu.edu.hk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：15A69 ; 15A60
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：1 November 2016
• 年：2016
• 卷：508
• 期：Complete
• 页码：100-132
• 全文大小：919 K

文摘

The main aim of this paper is to generalize matrix numerical ranges to the tensor case based on tensor norms. We show that the basic properties of matrix numerical ranges such as compactness and convexity are valid for tensor numerical ranges. We make use of convexity property to propose an algorithm for approximating tensor numerical ranges in which tensor eigenvalues are contained. Also we consider tensor numerical ranges based on inner products, however, they may not be convex in general.