[SciPy-user] ?ggev linalg.eig

[Pearu Peterson]

On Wed, 18 Sep 2002, Nils Wagner wrote:

> Hi,
> 
> I have used linalg.eig to compute the eigenvalues and left/right
> eigenvectors
> of a matrix pencil, that is
> 
> A x = lambda B x
> 
> A, B are real and nonsymmetric
> 
> w, vl, vr = linalg.eig(A,B,left=1,right=1)
> 
> However, I am puzzled by building the Rayleigh quotient R
> 
> z = dot(vl[:,i],dot(A,vr[:,i]))
> n = dot(vl[:,i],dot(B,vr[:,i]))
> R = z/n
> 
> Again, this should yield the eigenvalues but it doesn't. 
> Any idea ?

Why do you use in the definition of R both vl and vr?
AFAIK, R is defined through

z = dot(v[:,i],dot(A,v[:,i]))
n = dot(v[:,i],dot(B,v[:,i]))
R = z/n

where v is either vl or vr.

Pearu