We introduce and study an envelope-type region ɛ(A) in the complex plane that contains the eigenvalues of a given n×n complex matrix A. ɛ(A) is the intersection of an infinite number of regions defined by cubic curves. The notion and method of construction of ɛ(A) extend the notion of the numerical range of A, F(A), which is known to be an intersection of an infinite number of half-planes; as a consequence, ɛ(A) is contained in F(A) and represents an improvement in localizing the spectrum of A.
@article{bwmeta1.element.doi-10_2478_s11533-011-0111-2,
author = {Panayiotis Psarrakos and Michael Tsatsomeros},
title = {An envelope for the spectrum of a matrix},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {292-302},
zbl = {1242.15008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0111-2}
}
Panayiotis Psarrakos; Michael Tsatsomeros. An envelope for the spectrum of a matrix. Open Mathematics, Tome 10 (2012) pp. 292-302. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0111-2/
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