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From Sean Owen <sro...@gmail.com>
Subject Re: Using SVD-conditioned matrix
Date Sun, 16 Sep 2012 17:26:01 GMT
I don't quite get these formulations -- shouldn't Ak be in there
somewhere? you have a new row of that (well, some piece of some new
row of Ak), and need a new row of Uk. Or: surely the expression
depends on V?

On Sun, Sep 16, 2012 at 5:33 PM, Ted Dunning <ted.dunning@gmail.com> wrote:
> And if you want the reduced rank representation of A, you have it already
> with
>
>     A_k = U_k S_k V_k'
>
> Assume that A is n x m in size.  This means that U_k is n x k and V_k is m
> x k
>
> The rank reduced projection of an n x 1 column vector is
>
>     u_k = U_k U_k' u
>
> Beware that v_k is probably not sparse even if v is sparse.
>
> Similarly, the rank reduced projection of a 1 x m row vector is
>
>     v_k = v V_k V_k'
>
> A similar sparsity warning applies to v_k.  This is why it is usually
> preferable to just work in the reduced space directly.

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