The numerical range of 3 X 3 matrices

Dennis S. Keeler, Leiba Rodman, Ilya Spitkovsky

Research output: Contribution to journalArticle

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) 115-139 25 Linear Algebra and Its Applications 252 1-3 https://doi.org/10.1016/0024-3795(95)00674-5 Published - Jan 1 1997

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ASJC Scopus subject areas

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

Cite this

The numerical range of 3 X 3 matrices. / Keeler, Dennis S.; Rodman, Leiba; Spitkovsky, Ilya.

In: Linear Algebra and Its Applications, Vol. 252, No. 1-3, 01.01.1997, p. 115-139.

Research output: Contribution to journalArticle

Keeler, Dennis S. ; Rodman, Leiba ; Spitkovsky, Ilya. / The numerical range of 3 X 3 matrices. In: Linear Algebra and Its Applications. 1997 ; Vol. 252, No. 1-3. pp. 115-139.
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