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Re: Questions about "eigs"?
Posted:
Sep 24, 2013 11:20 AM


"Gergö " <schmidtg@stud.unihannover.de> wrote in message news:l1s450$ddp$1@newscl01ah.mathworks.com... > Hello, > > I am writing to you regarding two questions which arose when we were using > Matlab's "eigs" function. > > Question 1: How can it be achieved that "eigs" returns unnormalized > vektors? It normalize the vectors, at least when all eigenvalues are > computed.
In the situation where you ask for all or almost all the eigenvalues, EIGS calls EIG. If you ask for fewer eigenvalues, EIGS does not.
> Question 2: It seems that if "eigs" returns the k largest eigenvalues and > the corresponding vectors; and if we vary k: the sign of the eigenvectors > sometimes changes in dependency of k. Why is that the case?
If v is an eigenvector of A with eigenvalue d, we know that A*v = d*v. If c is a nonzero scalar, A*(c*v) = c*(A*v) = c*(d*v) = d*(c*v) so c*v is also an eigenvector of A with eigenvalue d. Let c = 1.
Calling EIGS multiple times, if you don't specify opts.v0, uses a random v0. That random v0 plus a change to the value of k may affect the signs of the eigenvectors or the values in the eigenvectors slightly due to taking a different path through the code; as long as A*V is "close to" V*D then the results are a valid set of eigenvalues and eigenvectors.
 Steve Lord slord@mathworks.com To contact Technical Support use the Contact Us link on http://www.mathworks.com



