[GAP Forum] Matrices that satisfy MM^T=I or MM^T=\lambda*I

[Philippe Cara (minitower)]

Hello Katie,

You might be interested in the 'forms' package wich can be found in the
packages section of http://www.gap-system.org

Forms is a package, developed by John Bamberg and
Jan De Beule. It can be used for work with sesquilinear and quadratic
forms, objects that are used to describe polar spaces and classical
groups. The package also deals with the recognition of certain matrix
groups preserving a sesquilinear or quadratic form. The main features
of forms are its facility with creating sesquilinear and quadratic
forms via matrices and polynomials, and in changing forms (creation of
isometries).

Best regards,

Philippe Cara


On Wed, 22 Dec 2010 07:40:36 -0600
Katie Morrison <kmorris2 at gmail.com> wrote:

> I understand that the general orthogonal group that GAP computes is
> not the group of matrices that satisfy MM^T=I because the GO group
> they compute actually leaves a different bilinear form fixed than the
> dot product.  But is there an easy way to find the group of matrices
> that satisfy MM^T=I and or to find the generalized version of this
> that satisfy MM^T=\lambda*I for some nonzero \lambda \in GF(q)?  A
> brute force search becomes completely unwieldy for matrices larger
> than 3 by 3, so if I can find some easy way to map from the general
> orthogonal group that GAP uses or find an efficient algorithm for
> computing this other group, that would be great.
> 
> Thanks,
> Katie Morrison
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