Numerical ranges of tensors

Rihuan Ke; Wen Li; Michael K. Ng

doi:10.1016/j.laa.2016.07.003

Numerical ranges of tensors

Rihuan Ke, Wen Li, Michael K. Ng^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

10 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	100-132
Number of pages	33
Journal	Linear Algebra and Its Applications
Volume	508
DOIs	https://doi.org/10.1016/j.laa.2016.07.003
Publication status	Published - 1 Nov 2016

User-Defined Keywords

Approximation
Convexity
Eigenvalues
Numerical range
Tensors

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10.1016/j.laa.2016.07.003

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AB - 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.

KW - Approximation

KW - Convexity

KW - Eigenvalues

KW - Numerical range

KW - Tensors

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JO - Linear Algebra and Its Applications

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ER -

Numerical ranges of tensors

Abstract

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