[R] order by which the eigenvalues are presented

Luis Borda de Agua lbagua at gmail.com
Wed May 6 18:58:50 CEST 2015

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

Luís Borda de Água
REFER Biodiversity Chair
CIBIO - Research Center in Biodiversity and Genetic Resources
Campus Agrário de Vairão
R. Padre Armando Quintas
4485-661 Vairão, 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

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