[SciPy-user] linalg.eig

[Pearu Peterson]

On Thu, 19 Sep 2002, Nils Wagner wrote:

> Hi,
> 
> To finish the discussion on linalg.eig ...
> 
> w, vl, vr = linalg.eig(A,B,left=1,right=1)
> 
> Please correct me, but I guess that the output of
> linalg.eig(A,B,left=1,right=1)
> is as follows
> 
> vr are the right eigenvectors
> 
> but vl are the complex c o n j u g a t e left eigenvectors

Yes, you are right. This is also what linalg.eig.__doc__ says.
Note that linalg.eig uses LAPACK convention. In matrix notation, we have
  w, vl, vr = linalg.eig(a,b,left=1,right=1)
such that
  a * vr = d * b * vr
  a^H * vl = d^H * b^H * vl   or  vl^H * a = d * vl^H * b
where `*' denotes matrix multiplication and d is a diagonal matrix of
eigenvalues: d = diag(w).

Pearu