[Bug-gsl] sign convention for eigenvectors in gsl_eigen_hermv

[Walter Hahn]

Dear all,

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. In other words, 
the matrix represents the tensor product of the first Pauli matrix four 
times with itself.

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 exept 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.

Thank you,
Walter

qu.cc
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