U = magic(4); %sample data
U = U(:,1:3); %non-square it
U'*(( U * U')\U) %see what happens:
ans =
1 -9.7145e-17 2.0817e-16
2.0817e-17 1 -1.6653e-16
1.3878e-17 8.3267e-17 1
the 10^-16 is just an artifact of floating point calculations. For all intensive purposes, the above is a 3x3 identity matrix.
Don't use inv, use '\'.
doc mldivide
