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 <[email protected]>: > > > On Feb 13, 2016, at 4:57 PM, Benoit Jacob <[email protected]> > 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: [email protected], Phone: ++1-970-4914288 > http://www.math.colostate.edu/~hulpke > > > _______________________________________________ Forum mailing list [email protected] http://mail.gap-system.org/mailman/listinfo/forum
