The numerical range of 3 X 3 matrices

Dennis S. Keeler; Leiba Rodman; Ilya M. Spitkovsky

doi:10.1016/0024-3795(95)00674-5

The numerical range of 3 X 3 matrices

Dennis S. Keeler, Leiba Rodman, Ilya M. Spitkovsky

Mathematics

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

Abstract

Let A be an n X n complex matrix. Then the numerical range of A, W(A), is defined to be {x*Ax : x ∈ ℂⁿ, x*x = 1}. In this article a series of tests is given, allowing one to determine the shape of W( A) for 3 X 3 matrices. Reconstruction of A, up to unitary similarity, from W(A) is also examined.

Original language	English (US)
Pages (from-to)	115-139
Number of pages	25
Journal	Linear Algebra and Its Applications
Volume	252
Issue number	1-3
DOIs	https://doi.org/10.1016/0024-3795(95)00674-5
State	Published - Feb 1997

ASJC Scopus subject areas

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

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10.1016/0024-3795(95)00674-5

Cite this

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title = "The numerical range of 3 X 3 matrices",

abstract = "Let A be an n X n complex matrix. Then the numerical range of A, W(A), is defined to be {x*Ax : x ∈ ℂn, x*x = 1}. In this article a series of tests is given, allowing one to determine the shape of W( A) for 3 X 3 matrices. Reconstruction of A, up to unitary similarity, from W(A) is also examined.",

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N2 - Let A be an n X n complex matrix. Then the numerical range of A, W(A), is defined to be {x*Ax : x ∈ ℂn, x*x = 1}. In this article a series of tests is given, allowing one to determine the shape of W( A) for 3 X 3 matrices. Reconstruction of A, up to unitary similarity, from W(A) is also examined.

AB - Let A be an n X n complex matrix. Then the numerical range of A, W(A), is defined to be {x*Ax : x ∈ ℂn, x*x = 1}. In this article a series of tests is given, allowing one to determine the shape of W( A) for 3 X 3 matrices. Reconstruction of A, up to unitary similarity, from W(A) is also examined.

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The numerical range of 3 X 3 matrices

Abstract

ASJC Scopus subject areas

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