On some 4-by-4 matrices with bi-elliptical numerical ranges

Titas Geryba; Ilya M. Spitkovsky

doi:10.1080/03081087.2020.1857326

On some 4-by-4 matrices with bi-elliptical numerical ranges

Titas Geryba, Ilya M. Spitkovsky

Mathematics

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

Abstract

A complete description of 4-by-4 matrices (Formula presented.), with scalar 2-by-2 diagonal blocks, for which the numerical range is the convex hull of two non-concentric ellipses is given. This result is obtained by reduction to the leading special case in which (Formula presented.) also is a scalar multiple of the identity. In particular cases when in addition (Formula presented.) is real or pure imaginary, the results take an especially simple form. An application to reciprocal matrices is provided.

Original language	English (US)
Pages (from-to)	855-870
Number of pages	16
Journal	Linear and Multilinear Algebra
Volume	69
Issue number	5
DOIs	https://doi.org/10.1080/03081087.2020.1857326
State	Published - 2021

Keywords

Numerical range
bi-elliptical shape
reciprocal matrix

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/03081087.2020.1857326

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abstract = "A complete description of 4-by-4 matrices (Formula presented.), with scalar 2-by-2 diagonal blocks, for which the numerical range is the convex hull of two non-concentric ellipses is given. This result is obtained by reduction to the leading special case in which (Formula presented.) also is a scalar multiple of the identity. In particular cases when in addition (Formula presented.) is real or pure imaginary, the results take an especially simple form. An application to reciprocal matrices is provided.",

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AU - Geryba, Titas

AU - Spitkovsky, Ilya M.

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AB - A complete description of 4-by-4 matrices (Formula presented.), with scalar 2-by-2 diagonal blocks, for which the numerical range is the convex hull of two non-concentric ellipses is given. This result is obtained by reduction to the leading special case in which (Formula presented.) also is a scalar multiple of the identity. In particular cases when in addition (Formula presented.) is real or pure imaginary, the results take an especially simple form. An application to reciprocal matrices is provided.

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KW - bi-elliptical shape

KW - reciprocal matrix

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On some 4-by-4 matrices with bi-elliptical numerical ranges

Abstract

Keywords

ASJC Scopus subject areas

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