[Numpy-discussion] matrix indexing question
Bill Baxter
wbaxter@gmail....
Fri Mar 30 00:46:32 CDT 2007
On 3/30/07, Timothy Hochberg <tim.hochberg@ieee.org> wrote:
>
>
> On 3/29/07, Bill Baxter <wbaxter@gmail.com> wrote:
> > On 3/30/07, Timothy Hochberg <tim.hochberg@ieee.org> wrote:
> > > Note, however that you can't (for instance) multiply column vector with
> > > a row vector:
> > >
> > > >>> (c)(r)
> > > Traceback (most recent call last):
> > > ...
> > > TypeError: Cannot matrix multiply columns with anything
> > >
> >
> > That should be allowed. (N,1)*(1,M) is just an (N,M) matrix with
> > entries C[i,j] = A[i,0]*B[0,]
>
> I thought about that a little, and while I agree that it could be allowed,
> I'm not sure that it should be allowed. It's a trade off between a bit of
> what I would guess is little used functionality with some enhanced error
> checking (I would guess that usually row*column signals a mistake). However,
> I don't care much one way or the other; it's not hard to allow.
>
It's useful for many things.
You can use it in the computation of the least squares best fits
between sets of points. The sum of p_i p_^t comes up in that
context. (Which is also the covariance matrix of the points)
The derivative of a unit vector (useful for mass spring dynamics
calcs, among other things, I'm sure) is given by something like c *
(I - x x^t).
Householder reflections are useful for a lot of things such as
implementing QR factorization. They're given by : H = I - 2 x x^t /
x^t x
http://www.cs.ut.ee/~toomas_l/linalg/lin2/node6.html
I'm positive I've seen col * row come up in other contexts too, though
I can't think of any other particulars right now.
--bb
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