[Numpy-discussion] [help needed] associativity and precedence of '@'

[Charles R Harris]

On Sat, Mar 15, 2014 at 1:29 PM, Nathaniel Smith <njs at pobox.com> wrote:

> On 15 Mar 2014 19:02, "Charles R Harris" <charlesr.harris at gmail.com>
> wrote:
> > Just to throw something new into the mix
> >
> >  u at v@w = u@(v at w) -- u at v is a dyadic matrix
> >
> >  u at v -- is a scalar
> >
> > It would be nice if u at v@None, or some such, would evaluate as a dyad.
> Or else we will still need the concept of row and column 1-D matrices. I
> still think v.T should set a flag so that one can distinguish u at v.T(dyad) from u.T at v(inner product), where 1-D arrays are normally treated as column vectors.
>
> This sounds important but I have no idea what any of it means :-) (What's
> a dyadic matrix?) Can you elaborate?
>

Dyadic matrices date back to the beginning of vector calculus and J. W.
Gibbs. These days they are usually written as v*w.T, i.e., the outer
product of two vectors and are a fairly common occurrence in matrix
expressions. For instance, covariance matrices  are defined as E(v * v.T)

Chuck
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