Find two matrix M and N

[boubekeur27]

non-singular matrices $M$ and $N$ such that :

$MEN=\begin{pmatrix}
1 & 0 & 0 & 0 \
0 &1 & 0 & 0 \
0 & 0& 0 & 0 \
0 & 0 & 0 & 0 \
\end{pmatrix} $
$E=\begin{pmatrix}
1 & 2 & 3 & 0 \
1 & 2 & 3 & 2 \
1 & 2 & 3 & 1 \
1 & 2 & 3 & 0 \
\end{pmatrix}$

[johanlofberg]

Well, the equality is just a nonlinear nonconvex quadratic constraint. Hard, but doable. The problem is non-singular, as that is almost impossible to represent (all matrices are arbitrarily close to being non-singular) so you will have to formulate in a better way such as N'*N=I or something like that

[boubekeur27]

Is this the solution?
n=4;
E=[-1 -1 -1 -2;4 3 2 5;-6 0 2 2;1 1 1 3];
op=rref([E,eye(n)]);
M=op(:,n+1:2n)
y=op(:,1:n);
z=rref([y,eye(n)]);
N=z(:,n+1:2n)

[johanlofberg]

I don't see what it has to do with YALMIP. If it solves your problem, well then by definition it is your solution