[Python-Dev] Matrix product

[Sebastien Loisel]

Dear Guido,

Thank you for your email.

On Tue, Jul 29, 2008 at 8:26 PM, Guido van Rossum <guido at python.org> wrote:
> But would it be totally outlandish to propose A**B for matrix
> multiplication? I can't think of what "matrix exponentiation" would
> mean...

Right now, ** is the pointwise power:

>>> from numpy import *
>>> A=array([[1,2],[3,4]])
>>> print(A**A)
[[  1   4]
 [ 27 256]]

Since all the scalar operators have meaning as pointwise operator,
like you say it's hard to bump one off to give it to the matrix
product instead. I don't know if it's a good idea with **, it will
destroy the orthogonality of the system.

They used to say, ignore LISP at your own peril. In that spirit, let
me describe MATLAB's approach to this. It features a complete suite of
matrix operators (+-*/\^), and their pointwise variants (.+ .- ./ .*
.^), although + and .+ are synonyms, as are - and.-. Right now,
numpy's *,**,/ correspond to MATLAB .*,.^,./.

MATLAB implements scalar^matrix, matrix^scalar, but not matrix^matrix
(although since log and exp are defined, I guess you could clobber
together a meaning for matrix^matrix). Since ^ is the matrix-product
version of "power", 2^A may not be what you expect:

>> 2^A
   10.4827   14.1519
   21.2278   31.7106

Sincerely,

-- 
Sébastien Loisel