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 nonzero complex parts. I am
wondering if eigenvectors of Hermitian matrix should all have zero imaginary
part or they can have nonzero imaginary parts as well.
Thanks,
Pinku agarwal
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