Uniqueness problem on numerical ranges of 3-by-3 companion matrices

Hsin Yi Lee

doi:10.1016/j.laa.2015.05.014

Uniqueness problem on numerical ranges of 3-by-3 companion matrices

Hsin Yi Lee

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Abstract For any two 3-by-3 companion matrices A and B with identical numerical ranges, we give a necessary and sufficient condition for A=B in terms of the shapes of numerical ranges and the locations of eigenvalues. In addition, all distinct 3-by-3 companion matrices with identical numerical ranges can be obtained precisely.

Original language	English
Article number	13216
Pages (from-to)	84-100
Number of pages	17
Journal	Linear Algebra and Its Applications
Volume	482
DOIs	https://doi.org/10.1016/j.laa.2015.05.014
State	Published - 1 Oct 2015

Keywords

Companion matrix
Numerical range
Uniqueness

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10.1016/j.laa.2015.05.014

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abstract = "Abstract For any two 3-by-3 companion matrices A and B with identical numerical ranges, we give a necessary and sufficient condition for A=B in terms of the shapes of numerical ranges and the locations of eigenvalues. In addition, all distinct 3-by-3 companion matrices with identical numerical ranges can be obtained precisely.",

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N2 - Abstract For any two 3-by-3 companion matrices A and B with identical numerical ranges, we give a necessary and sufficient condition for A=B in terms of the shapes of numerical ranges and the locations of eigenvalues. In addition, all distinct 3-by-3 companion matrices with identical numerical ranges can be obtained precisely.

AB - Abstract For any two 3-by-3 companion matrices A and B with identical numerical ranges, we give a necessary and sufficient condition for A=B in terms of the shapes of numerical ranges and the locations of eigenvalues. In addition, all distinct 3-by-3 companion matrices with identical numerical ranges can be obtained precisely.

KW - Companion matrix

KW - Numerical range

KW - Uniqueness

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DO - 10.1016/j.laa.2015.05.014

M3 - 期刊論文

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SN - 0024-3795

VL - 482

SP - 84

EP - 100

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

M1 - 13216

ER -

Uniqueness problem on numerical ranges of 3-by-3 companion matrices

Abstract

Keywords

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