I'm trying to calculate the SVD-decomposition of a certain matrix, i.e. $ A = U \Sigma V^T$.
My solution doesn't yield $A$ again; I just can't get the signs correct. I'm wondering if this is just a calculation error, or if I need to choose the eigenvectors in a special way.
Right now, I sorted the singular values, starting with the biggest. This determined the order of the eigenvectors which compose $V$. Whenever I had a choice, I chose the top components to be positive. For the not-yet determined eigenvectors of $U$, I chose the top component first $1$ and than $0$.
I don't think that this should matter but I'm looking for confirmation.