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.