SVD of a matrix from SVD of its columns

Question

Assume a matrix A, and I know the left singular vectors of SVD(A(:,i)), i=1,2,...,# of columns, is there a simple/fast transformation to obtain the left singular vectors of SVD(A) (the whole matrix)?

Answer 1

Absolutely not. The singular vectors of a single vector are trivial to calculate (there is a direct method you can use to do it). The singular vectors of a matrix are very hard to calculate (there is no, and there can be no, direct method if $n\geq 5$ where $n$ is the size of the matrix)