```
`enter code here`
cvx_begin
variables X(3) Y(3) Z(5) VX(L) VY(L) VZ(L)
asd = VX'*VY;
minimize (norm(S*X - VX,1)+norm(T*Y - VY,1)+norm(U*Z - VZ,1))
subject to
0 <= dot(VX,VY) <= 1;
0 <= dot(VX,VZ) <= 1;
0 <= dot(VY,VZ) <= 1;
cvx_end
```

Given S, T and U are vectors of some length L. Where VX = S*X; VY = T*Y, and VZ = U*Z actually. I want to obtain X,Y and Z such that the resultant VX, VY and VZ are mutually orthogonal. I have tried using many things but they are not helping. I would really appreciate your help if you could somehow re-frame the question so that I can achieve the aforementioned task.

Thank you.