Message-ID: <293DC84C-A5C5-4586-80FA-69199B7715E1@gmail.com>
Date: 2015-05-06T16:58:50Z
From: Luis Borda de Agua
Subject: order by which the eigenvalues are presented
Thank you, Bill, for your reply. However, I'm afraid I didn't explain myself properly.
Imagine you have a 2x2 matrix
Then the eigenvalues lambda_1 and lambda_2 are analytically calculated from
lambda_1 = (-b+sqrt(delta))/2a
lambda_2 = (-b-sqrt(delta))/2a
where delta = b^2-4ac
If delta>0 then lambda_1 > lambda_2 always. Otherwise their Real parts are equal.
If we have a 3x3 matrix the three eigenvalues will have very complicated expressions:
lambda_1 = f_1
lambda_2 = f_2
lambda_3 = f_3
where f_1,f_2 and f_3 are functions of the elements of the matrix a11,a12...,a33, which are sampled from a given distribution (e.g. normal(0,1)).
What I would like to know is from which expression (f_1,f_2 or f_3) comes the largest Re part of the eigenvalues. For example, does it always come from f_1 independently of the sampled values of a11,a12...,a33?
Thank you
____________________________________________________________
Lu?s Borda de ?gua
REFER Biodiversity Chair
CIBIO - Research Center in Biodiversity and Genetic Resources
Campus Agr?rio de Vair?o
R. Padre Armando Quintas
4485-661 Vair?o, Portugal
IICT - Tropical Research Institute
Travessa Conde da Ribeira N. 9 R/C
1300-142 Lisboa, Portugal
Tel: +351 21 361 63 40 ext. 312
[[alternative HTML version deleted]]