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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 |

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

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`

*Description:* Text Data

**[Bug-gsl] sign convention for eigenvectors in gsl_eigen_hermv**,
*Walter Hahn* **<=**