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. _______________________________________________ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion
