Orthonormal Basis from QR Decomposition

[victorvbc]

Hello everyone,

I'd like to ask for some help with a problem.

I want to get an orthonormal basis from the matrix [[1,-1,1],[3,-1,-1],[1,1,-3]], which has one linearly dependent column, so I use the QR decomposition to factor the matrix into orthogonal and upper trapezoidal parts. This results in the following Q and R matrices:

   

Unfortunately the Q matrix is singular, so I can't really use it. I know a decomposition with a complete orthogonal matrix is possible, from matlab:

   

So, is there a way I can get this to work on the Prime?

Edit: I've found a solution, It works if I use the uppercase QR() function.

Thanks,
-Victor.