[GAP Forum] Find rank-1 matrices in given subspace of matrices

[Benoit Jacob]

Hi Alexander,
That would give me the set of all rank-1 matrices. I want the set of those
rank-1 matrices that belong to some given linear subspace of matrices,
given e.g. as the span of a finite family of matrices.
Cheers,
Benoit

2016-02-15 11:53 GMT-05:00 Alexander Hulpke <hulpke at math.colostate.edu>:

>
> > On Feb 13, 2016, at 4:57 PM, Benoit Jacob <jacob.benoit.1 at gmail.com>
> wrote:
> >
> > Hello,
> >
> > What would be a good approach to obtain a parametrization of the set of
> all
> > rank-1 matrices in a given subspace of matrices M_n(F), where F is a
> finite
> > field?
>
> If you want nxm matrices over a field k, why not pick a random nonzero
> vector v\in k^n and a random normed (i.e. first nonzero coefficient is one)
> vector w\in k^m and form the (matrix) product v * w^T. I think this gives
> you a perfect parameterization via parameterizing v and w.
>
> Best,
>
>    Alexander Hulpke
>
> -- Colorado State University, Department of Mathematics,
> Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
> email: hulpke at math.colostate.edu, Phone: ++1-970-4914288
> http://www.math.colostate.edu/~hulpke
>
>
>