[R] order by which the eigenvalues are presented

[Luis Borda de Agua]

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


	[[alternative HTML version deleted]]