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 (US) |
|---|---|
| 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 | |
| State | Published - 2017 |
Publication series
| Name | Operator Theory: Advances and Applications |
|---|---|
| Volume | 259 |
| ISSN (Print) | 0255-0156 |
| ISSN (Electronic) | 2296-4878 |
Keywords
- Nilpotent matrix
- Numerical range
ASJC Scopus subject areas
- Analysis
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Militzer, E., Patton, L. J., Spitkovsky, I. M., & 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