the figure (fig_1) shown above is generate by this link that is trying to provide a reproduction (partly) to following wiki figure (fig_2) about svd
the direction of a basis vector (the black short one in fig_1) is opposite to the one ($\sigma_2$) in fig_2, does that matter for getting the new space (the right one in both fig_1 and fig_2)? I guess not, but why?