Is there any relationships of top-$k$ eigenvector and singular vector of symmetric matrix $A \in R^{n \times n}$?
For symmetric matrix $A$
its eigenvalue decomposition is:
$$ A = B \Lambda B^T$$
and its SVD is
$$A = U \Sigma V^T$$
Now I am interesting the top-$k$ ($k \ll n$) corresponding the top-$k$ eigenvalue or singular value.
The top-$k$ eigenvector:$B(1:k,:) \in R^{n \times k}$ and top-$k$ singular vector $U(1:k,:)\in R^{n \times k}$ . Is there any relationships between two matrices?
If given $U(1:k,:)$, can we get $B(1:k,:)$?