[GAP Forum] Diagonalize of symmetric matrix 248x248

[Dmitrii (Dima) Pasechnik]

Dear Marek,

On 13 January 2013 04:23, 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 eigenvalues (and, therefore, eigenvectors) need not be rational.
To achieve this, you might need to extend the field of rationals.

HTH,
Dmitrii

> 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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