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## [Help-gsl] Eigenvalues and eigenvectors of arbitrary complex valued matr

**From**: |
briccard |

**Subject**: |
[Help-gsl] Eigenvalues and eigenvectors of arbitrary complex valued matrix |

**Date**: |
Fri, 14 Feb 2014 18:31:38 +0100 |

**User-agent**: |
Mozilla/5.0 (Windows NT 6.1; rv:24.0) Gecko/20100101 Thunderbird/24.3.0 |

Hello,

`I searched the documentation and the forum but I cannot understand which
``method to use to determine eigenvalues/eigenvectors of an arbitrary
``complex valued square matrix (except for a message stating that it was
``not supported in 2007
``http://lists.gnu.org/archive/html/help-gsl/2007-05/msg00014.html).
`

`Looking at the section: "Complex Generalized Hermitian-Definite
``Eigensystems"
`
it states that this method solves the problem: *A x = \lambda B x***

`then I thought to set *A* as my matrix and *B* as the identity to revert
``to *A x = \lambda x* . The problem is that the function:
`

`int *gsl_eigen_genhermv* /(gsl_matrix_complex * A, gsl_matrix_complex *
``B, gsl_vector * eval, gsl_matrix_complex * evec,
``gsl_eigen_genhermv_workspace * w)
`
gives only real eigenvalues//, and then I got confused.
I don't understand some explanations of the documentation like:

`"Similarly to the real case, this can be reduced to *C y = \lambda y*
``where *C = L^{-1} A L^{-H}* is hermitian, and *y = L^H x*."
`

`Is there any other function (I saw that sometimes complex functions are
``not documented) to be used for this case?
``If not, it doesn't look like I can use the ///*C = L^{-1} A L^{-H}* /and
``//*/y = L^H x/* equations, identifying *C* as my original matrix, since
``it is stated that *C* is hermitian (am I right) and I do not understand
``what is the definition of the matrix *L* and the number *H*/.
`
Thanks for any help you can give me,
Riccardo Balzan

**[Help-gsl] Eigenvalues and eigenvectors of arbitrary complex valued matrix**,
*briccard* **<=**