[Numpy-discussion] matrix multiply

Alan G Isaac aisaac@american....
Sun Apr 6 15:34:10 CDT 2008

```On Sun, 6 Apr 2008, Charles R Harris wrote:
> The boolean  algebra is a field and the correct addition is xor, which is
> the same as addition modulo 2. This makes all matrices with determinant 1
> invertible. This isn't the current convention, however, as it was when
> Caratheodory was writing on measures and rings of sets were actually rings
> and the symmetric difference was used instead of union.

I am not sure what you are suggesting for matrix behavior,
nor what "correct" means here.

Comment:
Standard *boolean algebra* axioms include distributivity, but
1 xor (0 and 0) = 1 xor 0 = 1
(1 xor 0) and (1 xor 0) = 1 and 1 = 1

So I guess (?) what you are saying is something like:
if we have a boolen algebra with operators 'and' and 'or',
we can generate a boolean ring with operations 'xor' and 'and'.
When we do so, the '+' is traditionally used for the 'xor' operation.

But where in the modern literature on boolean matrices is
'+' given this interpretation?

IANAM,*
Alan Isaac

* IANAM = I am not a mathematician.

```