[Numpy-discussion] matrix multiply

Alan G Isaac aisaac@american....
Sun Apr 6 21:51:49 CDT 2008

On Sun, 6 Apr 2008, Anne Archibald apparently wrote:
> I am not aware of any algorithm for finding inverses, or 
> even determining which matrices are invertible, in the 
> peculiar Boolean arithmetic we use. 

Again, it is *not* peculiar, it is very standard for
boolean matrices.  And with this behavior, a nonnegative
integer power has an obvious graph theoretic interpretation.

Such boolean matrices are obviously invertible if they
are orthogonal.  It turn out this is a necessary condition
as well. [1]_  Orthogonality is obviously easy to test.

Alan Isaac

.. [1]
   Luce, D., 1952, "A Note on Boolean Matrix Theory",
   Proceeding of the Am. Math. Soc 3(3), p.382-8.

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