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From Ted Dunning <ted.dunn...@gmail.com>
Subject Re: Using SVD-conditioned matrix
Date Sun, 16 Sep 2012 23:11:07 GMT
On Sun, Sep 16, 2012 at 1:49 PM, Sean Owen <srowen@gmail.com> wrote:

> Oh right. It's the columns that are orthogonal. Cancel that.
>
> But how does this let you get a row of Uk out of a new row in Ak? Uk
> != Uk * Uk' * Ak
>

Well, actually, since a column of A is clearly in the space spanned by A so
if you take any such column, U_k U_k'  will send it back to where it came
from.  Thus,

  A_k = U_k U_k' A_k

If you want to talk about rows, then use V_k as with this:

  A_k = A_k V_k V_k'


Forgetting Sk, Uk = Ak * Vk, and I miss how these are equivalent so I
> misunderstand the intent of the expression.
>

Forgetting S_k is a bit dangerous here.  It is true that

    U_k S_k = A_k V_k

But, of course, right multiplying by V_k' gives us the identity above.

I think that the real confusion is that I am talking about projecting back
into span A and you are talking about expressing things in terms of the
latent variables.


> On Sun, Sep 16, 2012 at 8:55 PM, Ted Dunning <ted.dunning@gmail.com>
> wrote:
> > U_k ' U_k = I
> >
> > U_k U_k ' != I
>

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