Numerical ranges of tensors

Rihuan Ke; Wen Li; Kwok Po NG

doi:10.1016/j.laa.2016.07.003

Numerical ranges of tensors

Rihuan Ke, Wen Li, Kwok Po NG^*

^*Corresponding author for this work

Department of Mathematics

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

6 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

Scopus Subject Areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

User-Defined Keywords

Approximation
Convexity
Eigenvalues
Numerical range
Tensors

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10.1016/j.laa.2016.07.003

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AU - Li, Wen

AU - NG, Kwok Po

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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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DO - 10.1016/j.laa.2016.07.003

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VL - 508

SP - 100

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JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Numerical ranges of tensors

Abstract

Scopus Subject Areas

User-Defined Keywords

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