[Bug-gsl] sign convention for eigenvectors in gsl_eigen_hermv

[Walter Hahn]

Dear all,

a few weeks ago, I have sent you this bug report already without giving 
you enough information. Now, I would like to provide the missing 
information and correct some statements.

After using the procedure gsl_eigen_hermv to diagonalize a matrix, I 
suspect that the sign convention for the eigenvectors should be 
reconsidered. More specifically, I diagonalize a matrix which has only a 
few non-zero entries, namely at m(2i,2i+1) and m(2i+1,2i) for all i. In 
my case, I diagonalize a 8x8 matrix with real entries, e.g. 1.0.

The eigenvectors should be of the following form (not normalized):
v1=(1,1,0,0,0....)
v2=(-1,1,0,0,0,...),
other eigenvectors can be obtained by shifting the non-zero coefficients 
of v1 and v2 by two places to the right.

However, diagonalizing the 8x8 matrix described above, I obtain the 
eigenvectors as described above except the last one which is 
v8=(0,0,0,0,0,0,1,-1) instead of (0,0,0,0,0,0,-1,1), i.e., multiplied 
with (-1). Therefore, I think that the sign convention is either not 
implemented correctly or the convention used is not broad enough.

Please find in the attachment to this e-mail a simple compilable code 
which demonstrates this problem. I have checked the described results 
for GSL versions 1.15 and 1.16.

Kind regards,
Walter

qu.cc
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