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

[Katie Morrison]

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