1Department of Mathematics, Faculty of Exact Sciences, University Mustapha Stambouli of Mascara, Mascara, Algeria
Acta mathematica Universitatis Comenianae, Tome 89 (2020) no. 1, pp. 87-96
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Abdelkader Frakis; Abdelkader Frakis. New bounds for the spread of a matrix using the radius of the smallest disc that contains all eigenvalues. Acta mathematica Universitatis Comenianae, Tome 89 (2020) no. 1, pp. 87-96. http://geodesic.mathdoc.fr/item/AMUC_2020_89_1_a8/
@article{AMUC_2020_89_1_a8,
author = {Abdelkader Frakis and Abdelkader Frakis},
title = { New bounds for the spread of a matrix using the radius of the smallest disc that contains all eigenvalues},
journal = {Acta mathematica Universitatis Comenianae},
pages = {87--96},
year = {2020},
volume = {89},
number = {1},
url = {http://geodesic.mathdoc.fr/item/AMUC_2020_89_1_a8/}
}
TY - JOUR
AU - Abdelkader Frakis
AU - Abdelkader Frakis
TI - New bounds for the spread of a matrix using the radius of the smallest disc that contains all eigenvalues
JO - Acta mathematica Universitatis Comenianae
PY - 2020
SP - 87
EP - 96
VL - 89
IS - 1
UR - http://geodesic.mathdoc.fr/item/AMUC_2020_89_1_a8/
ID - AMUC_2020_89_1_a8
ER -
%0 Journal Article
%A Abdelkader Frakis
%A Abdelkader Frakis
%T New bounds for the spread of a matrix using the radius of the smallest disc that contains all eigenvalues
%J Acta mathematica Universitatis Comenianae
%D 2020
%P 87-96
%V 89
%N 1
%U http://geodesic.mathdoc.fr/item/AMUC_2020_89_1_a8/
%F AMUC_2020_89_1_a8
Let $\mathcal{D}$ denote the smallest disc containing alleigenvalues of the matrix $A$. Without knowing the eigenvalues of$A$, we can estimate the spread of $A$ and the radius of$\mathcal{D}$. Some new bounds for the radius of $\mathcal{D}$ andthe spread of $A$ are given. These bounds involve the entries of$A$. Also sufficient conditions for equality are obtained for someinequalities. New proofs of some known results are presented too.
