It is possible to orthogonalize a set of linearly independent vectors via SVD? Let's say I have a set of linearly independent vectors, collected in a square matrix $\mathbf{M}$.
I know that I could orthogonalize these vectors with the QR decomposition,
$\mathbf{M} = \mathbf{QR}$
where $\mathbf{Q}$ is my orthogonal set of vectors.
I'm curious if it is possible to do the same with the SVD, but I cannot figure out how. 
I want to know how to go from $\mathbf{M}$ to $\mathbf{Q}$, using SVD instead of QR.
If this is not possible, I'd like to know as well.

If $M$ is a matrix of $k$ linearly independent columns with SVD $M = U \Sigma V^H$, then the first $k$ columns of $U$ form an orthonormal basis for the span of the columns of $M$.
