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[Bug-gsl] sign convention for eigenvectors in gsl_eigen_hermv

From: Walter Hahn
Subject: [Bug-gsl] sign convention for eigenvectors in gsl_eigen_hermv
Date: Tue, 04 Feb 2014 14:50:44 +0100
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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):
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,

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