Discussion: new operators for numerical computation

[Tim Hochberg]

Robin Becker <robin at jessikat.fsnet.co.uk> writes:
[...] 
> We have three common multiplies for matrices and I claim that n vectors
> are n by 1 matrices.  I agree that for higher order tensors the outer
> product is more complicated, but see 
> 
>         http://mathworld.wolfram.com/TensorDirectProduct.html

Unfortunately, (or fortunately depending on your point of view) none
(?)  matrix types floating around PyLand right now have a notion of
Contravariant or Covariant indices.

[I vaguely recall Konrand's Scientific Python package having something
in this vein although I could easily be wrong]

> the kronecker product is also called the matrix direct product
> 
> 
> A ox B = [a11 B a12 B]
>          [a12 B a22 B]
> 
> seems to me to be like a tensor outer product; but I ain't no
> mathematician ;)

Very odd indeed. (Just in case anyone else was confused, that's a11*B
and a12*B etc.)

> 
> the lie product (or bracket) has applications in sensitivity analysis
> and other more exotic stuff in differential geometry
> 
> [A,B] = AB - BA

It's the commutator! Why didn't anyone say so earlier. 

-tim