[GAP Forum] Diagonalize of symmetric matrix 248x248

[Marek Mitros]

In general you are right. In this case I've got information from G. Nebe,
that matrix is diagonalizable over rationals. So orthogonal representation
of Th group would have rational entries.

Regards,
Marek
13-01-2013 07:29, "Dmitrii (Dima) Pasechnik" <dima at ntu.edu.sg> napisał(a):

> 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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