[GAP Forum] Square root of cyclotomic real number

[Max Horn]

> On 19 May 2016, at 07:48, Marek Mitros <marek at mitros.org> wrote:
> 
> Thank you for advice. Let me explain my plan, then we can judge whether
> this advice work for me or it doesn't.
> 
> I have group of size 5120 of complex matrices of size 16x16. In this group
> I listed two conjugacy classes of involutions of size 10 and 80. Next I
> wanted to change the basis in a way that mentioned 10 matrices are
> diagonal. Therefore I obtained 16 vectors as intersections of eigenspaces.
> Unfortunately these vectors are not unit length, so I tried to normalize
> them.

You don't need to normalize them in order to construct an orthogonal basis -- that is only necessary for an orthonormal basis. So if you really just need a base change to diagonalize your matrices, that is possible without computing squares and normed vectors.

Cheers,
Max