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

Ilya Spitkovsky, Claire Marie Thomas

Research output: Contribution to journalArticle

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 languageEnglish (US)
Article number46
Pages (from-to)693-703
Number of pages11
JournalElectronic Journal of Linear Algebra
Volume30
DOIs
StatePublished - Oct 4 2015

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Numerical Range
Tridiagonal matrix
Line segment
Geometric progression
Zero

Keywords

  • Flat portions
  • Numerical range
  • Tridiagonal matrices

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Line segments on the boundary of the numerical ranges of some tridiagonal matrices. / Spitkovsky, Ilya; Thomas, Claire Marie.

In: Electronic Journal of Linear Algebra, Vol. 30, 46, 04.10.2015, p. 693-703.

Research output: Contribution to journalArticle

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