Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897899 | Linear Algebra and its Applications | 2018 | 24 Pages |
Abstract
For a given n-by-n matrix A, its normalized numerical rangeFN(A) is defined as the range of the function fN,A:xâ¦(xâAx)/(âAxââ
âxâ) on the complement of kerâ¡A. 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:R3â¦C.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Brian Lins, Ilya M. Spitkovsky, Siyu Zhong,