Find non-trivial solution

Find non-trivial solution

[wwfarch]

I'm having an issue with GSL and solving homogeneous systems. In
particular I have an equation of the form:

Av = 0

where A is an Nx6 matrix, v is a vector (size 6) and 0 represents a zero
vector.

Regardless of N when I solve for v I always get the trivial solution (v
= 0). Is there a way to force GSL to provide a non-trivial solution?
Once I have a non-trivial solution I can scale as I need to for my
application. As a note, when N>6 I solve with a least squares solution.
I've tried QR and SVD decompositions.

Thanks,
Matthew Parent

Re: Find non-trivial solution

[Brian Gough]

At Thu, 03 Aug 2006 14:43:49 -0400,
wwfarch@rochester.rr.com wrote: 
> I'm having an issue with GSL and solving homogeneous systems. In
> particular I have an equation of the form: Av = 0 where A is an Nx6
> matrix, v is a vector (size 6) and 0 represents a zero vector.
> 
> Regardless of N when I solve for v I always get the trivial solution (v
> = 0). Is there a way to force GSL to provide a non-trivial solution?
> Once I have a non-trivial solution I can scale as I need to for my
> application. As a note, when N>6 I solve with a least squares solution.
> I've tried QR and SVD decompositions.

Hello,
The _solve functions do back-substitution so will always give v=0 for
a zero rhs. If you want to find the null space of A, use the SVD to
get a basis for it from the columns of V corresponding to the zero
singular values.

-- 
Brian Gough

Network Theory Ltd,
Publishing the GSL Manual - http://www.network-theory.co.uk/gsl/manual/