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Orthonormal Basis from QR Decomposition - victorvbc - 06-06-2020 03:39 PM

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.