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" <d...@ntu.edu.sg> napisał(a): > Dear Marek, > > On 13 January 2013 04:23, Marek Mitros <ma...@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 > > > > _______________________________________________ > > Forum mailing list > > Forum@mail.gap-system.org > > http://mail.gap-system.org/mailman/listinfo/forum > > CONFIDENTIALITY:This email is intended solely for the person(s) named and > may be confidential and/or privileged.If you are not the intended > recipient,please delete it,notify us and do not copy,use,or disclose its > content. > > Towards A Sustainable Earth:Print Only When Necessary.Thank you. > _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
