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

Erin Militzer; Linda J. Patton; Ilya M. Spitkovsky; Ming Cheng Tsai

doi:10.1007/978-3-319-49182-0_23

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

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

General Education Center

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

6 Scopus citations

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 language	English
Title of host publication	Operator Theory
Subtitle of host publication	Advances and Applications
Publisher	Springer International Publishing
Pages	561-591
Number of pages	31
DOIs	https://doi.org/10.1007/978-3-319-49182-0_23
State	Published - 2017

Publication series

Name	Operator Theory: Advances and Applications
Volume	259
ISSN (Print)	0255-0156
ISSN (Electronic)	2296-4878

Bibliographical note

Publisher Copyright:
© 2017 Springer International Publishing.

Keywords

Nilpotent matrix
Numerical range

Access to Document

10.1007/978-3-319-49182-0_23

Cite this

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Numerical ranges of 4-By-4 nilpotent matrices: Flat portions on the boundary. / Militzer, Erin; Patton, Linda J.; Spitkovsky, Ilya M. et al.
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 proceeding › Chapter › peer-review

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

Abstract

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Keywords

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