let $v$ be a vector, and $\forall i \in 1..k < n : n_i$ be normal vectors of hyperplanes in the in an $R^n$ space. the problem is to compute orthogonal Projection of $v$ onto intersection of all those planes.
I'm looking for an n*n matrix (M), so that $vM = Projection(v)$
Here are two examples: $$n=3, k=2, n_1=(1,0,0), n_2=(0,1,0) \Rightarrow p(1,1,1) = (0,0,1)$$$$n=3,k=2,n_1=(1,0,-1),n_2=(0,1,-1) \Rightarrow p(0,0,1)=({1 \over 3},{1 \over 3},{1 \over 3})$$$$n=3,k=1,n_1=(0,0,1) \Rightarrow p(1,1,1) = (1,1,0)$$