Henning Thielemann wrote:
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.
So the linear operator is translation (ie: + v)... effectively 'plus' could be viewed as a function which takes a vector and returns a matrix (operator) (+) :: Vector -> Matrix Which could also be called 'translate'. So 'translate' takes a vector and returns a linear-operator which can be applied to a vector: mapply (translate vector1) vector2 So I guess I could now ask, why allow vector addition at all? Keean.