Numerical ranges of 4-By-4 nilpotent matrices: Flat portions on the boundary

Erin Militzer, Linda J. Patton, Ilya Spitkovsky, Ming Cheng Tsai

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In their 2008 paper Gau and Wu conjectured that the numerical range of a 4-by-4 nilpotent matrix has at most two flat portions on its boundary. We prove this conjecture, establishing along the way some additional facts of independent interest. In particular, a full description of the case in which these two portions indeed materialize and are parallel to each other is included.

Original languageEnglish (US)
Title of host publicationOperator Theory
Subtitle of host publicationAdvances and Applications
PublisherSpringer International Publishing
Pages561-591
Number of pages31
DOIs
StatePublished - Jan 1 2017

Publication series

NameOperator Theory: Advances and Applications
Volume259
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

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Nilpotent Matrix
Numerical Range

Keywords

  • Nilpotent matrix
  • Numerical range

ASJC Scopus subject areas

  • Analysis

Cite this

Militzer, E., Patton, L. J., Spitkovsky, I., & Tsai, M. C. (2017). Numerical ranges of 4-By-4 nilpotent matrices: Flat portions on the boundary. In Operator Theory: Advances and Applications (pp. 561-591). (Operator Theory: Advances and Applications; Vol. 259). Springer International Publishing. https://doi.org/10.1007/978-3-319-49182-0_23

Numerical ranges of 4-By-4 nilpotent matrices : Flat portions on the boundary. / Militzer, Erin; Patton, Linda J.; Spitkovsky, Ilya; Tsai, Ming Cheng.

Operator Theory: Advances and Applications. Springer International Publishing, 2017. p. 561-591 (Operator Theory: Advances and Applications; Vol. 259).

Research output: Chapter in Book/Report/Conference proceedingChapter

Militzer, E, Patton, LJ, Spitkovsky, I & Tsai, MC 2017, Numerical ranges of 4-By-4 nilpotent matrices: Flat portions on the boundary. in Operator Theory: Advances and Applications. Operator Theory: Advances and Applications, vol. 259, Springer International Publishing, pp. 561-591. https://doi.org/10.1007/978-3-319-49182-0_23
Militzer E, Patton LJ, Spitkovsky I, Tsai MC. Numerical ranges of 4-By-4 nilpotent matrices: Flat portions on the boundary. In Operator Theory: Advances and Applications. Springer International Publishing. 2017. p. 561-591. (Operator Theory: Advances and Applications). https://doi.org/10.1007/978-3-319-49182-0_23
Militzer, Erin ; Patton, Linda J. ; Spitkovsky, Ilya ; Tsai, Ming Cheng. / Numerical ranges of 4-By-4 nilpotent matrices : Flat portions on the boundary. Operator Theory: Advances and Applications. Springer International Publishing, 2017. pp. 561-591 (Operator Theory: Advances and Applications).
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