On 06/05/2015 12:58 PM, Luis Borda de Agua wrote: > 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.
The first condition is incomplete. You need a>0 as well. > > > > 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? I don't know the answer, but I would expect it to depend on the entries in the matrix in quite a complicated way. Duncan Murdoch ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
