On Fri, 8 Jul 2005, Keean Schupke wrote: > Henning Thielemann wrote: > > >Do you mean > > [x,y,z,1] * [[1,0,0,0],[0,1,0,0],[0,0,1,0],[dx,dy,dz,dw+1]] > >? > > > Erm, yes thats what I meant ... but you obviously got the point. > > >>but how is this different from adding vectors? If we allow vector > >>addition then we no longer have the nice separation between values and > >>linear operators, as a value can also be a linear operator (a > >>translation)? > > > >??? > > Well if a vector can be a linear-operator, then surely it _is_ a matrix!
In general a vector need not to be a linear operator. You talked about vector translation, translation is not a linear operator. You gave some process to map the problem to somewhere, where it becomes a linear operator. Other people said that the scalar product with a fixed vector is a linear operator. That's true. Now what is a natural interpretation of a vector as linear operator? The scalar product or the translation? Vectors can be used and abused for many things but an object which can be called a vector (because of its ability of to be added and to be scaled) is not a linear operator itself and does not naturally represent one. _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe