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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, 18 Feb 2014 18:43:48 +0100 |

**User-agent**: |
Mozilla/5.0 (X11; Linux x86_64; rv:17.0) Gecko/20131103 Icedove/17.0.10 |

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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