---
_id: '1640772'
abstract:
- lang: eng
text: 'Let Sigma be a bounded set of complex matrices, Sigma(m) = {A(1)...A(m) :
A(i) is an element of Sigma}. The generalized spectral-radius theorem states that
rho(Sigma)= <(rho)over cap>(Sigma), where rho(Sigma) and <(rho)over cap>(sigma)
are defined as follows: rho(Sigma) = lim sup rho(m)(Sigma){1/m}, where rho(m)(Sigma)
= sup {rho(A) : A is an element of Sigma(m)} with rho (A) the spectral radius;
<(rho)over cap>(Sigma) = lim sup <(rho)over cap>(m)(Sigma){1/m}, where <(rho)over
cap>(m)(Sigma) = sup {parallel to A parallel to: A is an element of Sigma(m)}
with parallel to parallel to any matrix norm. We give an elementary proof, based
on analytic and geometric tools, which is in some ways simpler than the first
proof by Berger and Wang.'
author:
- first_name: Ludwig
full_name: Elsner, Ludwig
id: '10509'
last_name: Elsner
citation:
ama: 'Elsner L. The generalized spectral-radius theorem: An analytic-geometric proof.
*Linear Algebra and its Applications*. 1995;220:151-159.'
angewandte-chemie: 'L. Elsner, “The generalized spectral-radius theorem: An analytic-geometric
proof”, *Linear Algebra and its Applications*, **1995**, *220*,
151-159.'
apa: 'Elsner, L. (1995). The generalized spectral-radius theorem: An analytic-geometric
proof. *Linear Algebra and its Applications*, *220*, 151-159. doi:10.1016/0024-3795(93)00320-Y'
apa_indent: 'Elsner,
L. (1995). The generalized spectral-radius theorem: An analytic-geometric proof.
*Linear Algebra and its Applications*, *220*, 151-159. doi:10.1016/0024-3795(93)00320-Y

'
bio1: 'Elsner L (1995)

The generalized spectral-radius theorem: An analytic-geometric
proof.

Linear Algebra and its Applications 220: 151-159.'
chicago: 'Elsner,
Ludwig. 1995. “The generalized spectral-radius theorem: An analytic-geometric
proof”, Linear Algebra and its Applications, 220: 151-159.

'
default: 'Elsner L (1995)

*Linear Algebra and its Applications* 220:
151-159.'
dgps: 'Elsner,
L. (1995). The generalized spectral-radius theorem: An analytic-geometric proof
(Linear Algebra and its Applications), *220*, 151-159. Gehalten auf der
International Workshop on Nonnegative Matrices, Applications and Generalizations
and 8th Haifa Matrix Theory Conference, ELSEVIER SCIENCE PUBL CO INC. doi:10.1016/0024-3795(93)00320-Y.

'
frontiers: 'Elsner, L. (1995). The generalized spectral-radius theorem: An analytic-geometric
proof. *Linear Algebra and its Applications* 220, 151-159.'
harvard1: 'Elsner, L., 1995. The generalized spectral-radius theorem: An analytic-geometric
proof. *Linear Algebra and its Applications*, 220, p 151-159.'
ieee: ' L. Elsner, “The generalized spectral-radius theorem: An analytic-geometric
proof”, *Linear Algebra and its Applications*, vol. 220, 1995, pp. 151-159.'
lncs: ' Elsner, L.: The generalized spectral-radius theorem: An analytic-geometric
proof. Linear Algebra and its Applications. 220, 151-159 (1995).'
mla: 'Elsner, Ludwig. “The generalized spectral-radius theorem: An analytic-geometric
proof”. *Linear Algebra and its Applications* 220 (1995): 151-159.'
wels: 'Elsner, L. (1995): The generalized spectral-radius theorem: An analytic-geometric
proof *Linear Algebra and its Applications*,220: 151-159.'
conference:
end_date: 1993-06-10
location: Haifa, Israel
name: International Workshop on Nonnegative Matrices, Applications and Generalizations
and 8th Haifa Matrix Theory Conference
start_date: 1993-05-31
date_created: 2010-04-29T13:15:58Z
date_updated: 2019-07-11T10:06:13Z
department:
- _id: '10020'
doi: 10.1016/0024-3795(93)00320-Y
external_id:
isi:
- A1995RC37100008
intvolume: ' 220'
isi: 1
language:
- iso: eng
page: 151-159
publication_identifier:
issn:
- 0024-3795
publication_status: published
publisher: ELSEVIER SCIENCE PUBL CO INC
quality_controlled: '1'
series_title: Linear Algebra and its Applications
status: public
title: 'The generalized spectral-radius theorem: An analytic-geometric proof'
type: conference
user_id: '67994'
volume: 220
year: '1995'
...