Suppose I have an $d\times d$ real-valued matrix $A$. How can I approximate $d$ column norms of $A$ by utilizing a small number of calls to matrix-vector product, $f(x)=Ax$?
There are results$^1$relying on vector-matrix products $g(y)=y'A$ but I can't find anything relevant to matrix-vector product, any tips?
$^1$: $d$ calls to $g(y)$ project columns to a $d$-dimensional subspace, can use JL lemma for random $y$'s or Rudelson/Vershynin for crafted $y$'s