I think yes, cuz it preserves both addition and scalar multiplication properties.
Alex
Seems arbitrary to be on the unit interval but I suppose that's just for convenience?
whc
Is there some equivalent concept of a matrix for a function?
auruxy
I would say that it would be the case. Integrals themselves are linear transformations since they can be "split" up (integrated over the sum of the functions or a sum of the integral of each function) and you can insert a scalar inside the integral. Just like derivatives.
I think it is
I think yes, cuz it preserves both addition and scalar multiplication properties.
Seems arbitrary to be on the unit interval but I suppose that's just for convenience?
Is there some equivalent concept of a matrix for a function?
I would say that it would be the case. Integrals themselves are linear transformations since they can be "split" up (integrated over the sum of the functions or a sum of the integral of each function) and you can insert a scalar inside the integral. Just like derivatives.