[GAP Forum] Diagonalize of symmetric matrix 248x248

[Marek Mitros]

Hello again,

I would like to thank you all the people who answered on my post.
Thanks to Gabrielle Nebe I was able to obtain orthogonal
representation of Th group. This makes me happy and I am able to
continue my research in this group.

My method was wrong. You do not need to look for eigenvectors of Gram
matrix in order to do orthogonalization. Prof. Nebe has sent me the
magic matrix using which I obtained orthogonal generators from the
linear ones present on lattice catalogue web page.

Best regards,
Marek Mitros


On 1/12/13, Mathieu Dutour <mathieu.dutour at gmail.com> wrote:
> Maybe you can try to use real arithmetic for diagonalization using a
> Fortran code that implement Jacobi method.
>
> Otherwise, I am not sure if such a diagonalization makes sense.
> Such gram matrix are defined up to arithmetic equivalence
> A ---> PAP^T   with P an integral matrix of determinant +-1.
> The matrix on Nebe's website is just one matrix in the whole equivalence
> class and the eigenvalues will be different if you choose another matrix in
> the equivalence class.
>
>   Mathieu
>
>
>
> On Sat, Jan 12, 2013 at 9:23 PM, Marek Mitros <marek at mitros.org> wrote:
>
>> Hi,
>>
>> What is the quickest way to diagonalize symmetric matrix 248x248 with
>> integral entries. I run Eigenvectors(Rationals, m) but it run long
>> time on my PC. The matrix is the Gram matrix of Thompson Smith lattice
>> in dimension 248. See page:
>> http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/TH.html
>>
>> I would like to obtain the lattice generators or alternatively
>> orthogonal representation of Thompson sporadic group.
>>
>> Regards,
>> Marek
>>
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>