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
>
