Line segments on the boundary of the numerical ranges of some tridiagonal matrices

Ilya M. Spitkovsky; Claire Marie Thomas

doi:10.13001/1081-3810.3012

Line segments on the boundary of the numerical ranges of some tridiagonal matrices

Ilya M. Spitkovsky, Claire Marie Thomas

Mathematics

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

Abstract

Tridiagonal matrices are considered for which the main diagonal consists of zeroes, the sup-diagonal of all ones, and the entries on the sub-diagonal form a geometric progression. The criterion for the numerical range of such matrices to have line segments on its boundary is established, and the number and orientation of these segments is described.

Original language	English (US)
Article number	46
Pages (from-to)	693-703
Number of pages	11
Journal	Electronic Journal of Linear Algebra
Volume	30
DOIs	https://doi.org/10.13001/1081-3810.3012
State	Published - Oct 4 2015

Keywords

Flat portions
Numerical range
Tridiagonal matrices

ASJC Scopus subject areas

Algebra and Number Theory

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10.13001/1081-3810.3012

Cite this

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abstract = "Tridiagonal matrices are considered for which the main diagonal consists of zeroes, the sup-diagonal of all ones, and the entries on the sub-diagonal form a geometric progression. The criterion for the numerical range of such matrices to have line segments on its boundary is established, and the number and orientation of these segments is described.",

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Line segments on the boundary of the numerical ranges of some tridiagonal matrices

Abstract

Keywords

ASJC Scopus subject areas

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