Journal article
Matrices with rotation and/or reflection invariant higher rank numerical ranges
Linear & multilinear algebra, pp 1-24
02 Jul 2025
Abstract
We show that two πΓπ matrices have the same Kippenhahn polynomial if and only if they (1) have the same trace and (2) have the same rank-k numerical ranges for 1β€πβ€β
π
2
β. In addition to this result, we provide a second necessary and sufficient condition for an πΓπ matrix to have higher rank numerical ranges that are invariant under rotations by 2β’π/β for some integer ββ₯2. Finally, we adapt this result to provide another necessary and sufficient condition for an πΓπ matrix to have higher rank numerical ranges that are invariant under reflection over the real axis.
Metrics
2 Record Views
Details
- Title
- Matrices with rotation and/or reflection invariant higher rank numerical ranges
- Creators
- Sarah Gift - Drexel UniversityHugo J. Woerdeman - Drexel University
- Publication Details
- Linear & multilinear algebra, pp 1-24
- Publisher
- Taylor & Francis
- Number of pages
- 24
- Grant note
- National Science Foundation: 6.1
We would like to thank the referee for their extensive report and helpful suggestions. In particular, they referred us to Gau and Wu's 2013 paper [20], which led to the inclusion of Section 3 and allowed us to strengthen Theorems 4.2, 5.1, and 6.1.
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:001521887100001
- Scopus ID
- 2-s2.0-105009737290
- Other Identifier
- 991022061533004721