orthogonal eigenvectors with zgeev

[wsim83]

Hi, I'm in need of orthogonal eigenvectors. I'm wondering if zgeev should produce a complete set of orthogonal eigenvectors within degenerate subspaces( as zheev does) or if I have to orthogonalize by hand. Is there a routine that would finish off the orthogonalization?
William

[sven]

Hi William,

Unless there is something special about your matrix, a non-Hermitian matrix will not usually have orthogonal eigenvectors. If you are looking for an orthonormal basis for the invariant subspace spanned by the eigenvalues, then you can use ZGEES, or ZGEESX, to find the Schur vectors.

Best wishes,

Sven Hammarling,

[wsim83]

Hi Sven,
The matrix I am testing my programming with is hermitian. zheev produces orthogonal eigenvectors but zgeev does not seem to. The reason I'm testing with zgeev is that later I will need to diagonalize the same matrix multiplied by diag(1...1,-1...-1).

[sven]

Hi William,

zgeev does not diagonalize a matrix, it uses the Schur factorization and in general it does not produce orthogonal eigenvectors.

Are you multiplying on just one side by diag(1...1,-1...-1)? What is it that you are trying to achieve?

Best wishes,

Sven.

[wsim83]

Hi Sven,

I want to obtain the eigenvalues and eigenvectors of J*H, H is Hermitian, so that I can evaluate thermal averages of bilinear forms of boson operators. The condition on the eigenvectors is that they satisfy
conjTrans(vi)*J*vj = (-1)^(a)*delta_{ij}, where a=(o for i =1,...N and 1 for i=N+1,..., 2N) and vi,vj are eigenvectors. For the condition to be satisfied I think I need orthogonal eigenvectors.

William

[Julien Langou]

Your matrix is Hamiltonian I believe. Please have a look at HAPACK.
http://www.tu-chemnitz.de/mathematik/hapack/
An excellent reference is the PhD thesis of Daniel Kressner Section 4.3, 4.4 and 4.5.
Best wishes,
Julien.