Abstract
For a given n-by-n matrix A, its normalized numerical range FN(A) is defined as the range of the function fN,A:x↦(x⁎Ax)/(‖Ax‖⋅‖x‖) on the complement of kerA. We provide an explicit description of this set for the case when A is normal or n=2. This extension of earlier results for particular cases of 2-by-2 matrices (by Gevorgyan) and essentially Hermitian matrices of arbitrary size (by A. Stoica and one of the authors) was achieved due to the fresh point of view at FN(A) as the image of the Davis–Wielandt shell DW(A) under a certain non-linear mapping h:R3↦C.
Original language | English (US) |
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Pages (from-to) | 187-209 |
Number of pages | 23 |
Journal | Linear Algebra and Its Applications |
Volume | 546 |
DOIs | |
State | Published - Jun 1 2018 |
Keywords
- Davis–Wielandt shell
- Normal matrix
- Normalized numerical range
ASJC Scopus subject areas
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics