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[Lapack] Lapack Subroutine ZHEEV


All the eigenvalues of a complex Hermitian matrix are real, (by theorem,)
so in addition you have all eigenvectors of this matrix to have zero imaginary 
part 
(i.e., these vectors are real), then the initial complex Hermitian matrix is 
indeed
real symmetric since A = V D V^H and V and D are real. So to restate 
differently, 
if you start with a complex Hermitian matrix where at least one entry of this 
matrix is complex, 
you are sure that at least one entry in the eigenvector matrix V needs to be 
complex. 
Cheers,
Julien.

On Jan 13, 2013, at 5:17 PM, Pinku Agarwal wrote:

Hi,

I am using lapack complex Hermitian solver ZHEEV to calculate eigenvectors of 
complex hermitian Matrix. All the eigenvectors that I am getting are 
orthogonal to each other but some of them have non-zero complex parts. I am 
wondering if eigenvectors of Hermitian matrix should all have zero imaginary 
part or they can have non-zero imaginary parts as well.

Thanks,
Pinku agarwal
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