14 May
2013
14 May
'13
10:29 a.m.
A *comatrix* consists of three sets X, Y, and S, and two functions f:X -> S, g:Y -> S. We can define composition of comatrices A=(X,Y,S,f,g) and B=(Y,Z,T,h,j) by B o A = (X, Z, (T+S)/g(y)~h(y), f, j). I made up the name above. Does anyone know this construction under a different name? I suspect it might be used in dealing with sparse matrices somewhere, since when all the sets are finite, g x h:Y -> S x T can be thought of as a matrix where the (s,t) element is the size of the preimage of (s,t) under g x h. Then (T+S)/g(y)~h(y) is a measure of how many nonzero elements there are. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com