On Sat, Mar 15, 2014 at 1:29 PM, Nathaniel Smith <njs@pobox.com> wrote:
On 15 Mar 2014 19:02, "Charles R Harris" <charlesr.harris@gmail.com> wrote:
Just to throw something new into the mix
u@v@w = u@(v@w) -- u@v is a dyadic matrix
u@v -- is a scalar
It would be nice if u@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@v.T(dyad) from u.T@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