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

[Alexander Hulpke]

> 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,
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email: hulpke at math.colostate.edu, Phone: ++1-970-4914288
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