I'm dealing here with the following problem: I have a complex matrix $F$, having size $N \times M$, with $N<<M$. I can easily compute a basis of the null space of $F$, i.e. the space of vectors $x$ such that $Fx=0_v$, where $0_v$ denotes the $N \times 1$ column vector of all zeros.
However, I'm interested to specific solutions of the $Fx=0_v$ problem, i.e. to the vector(s) $x$ such that $\left|x_i\right|=1$ for $i=1,...,M$. I'm seeking vectors having constant amplitude.
Do you have any insights? Thanks