I was reading a paper and going through the definition part.
For first paragraph, since B is a matrix with orthonormal columns, wouldnt $BB^{T} = I_{d\times d}$ ?
For second paragraph, note that the span{$v_{i} | i\in [k]$} refer to the span of the k right singular vectors of A corresponding to highest k singluar value. And so how does it make sense of 'projecting the rows onto some span of some span of right singular vectors (of A)"?
Thanks in advance.