list 3 operations that satisfy the following rule:

h(a+b-c) = h(a)+h(b)-h(c)

Question

list 3 operations that satisfy the following rule:

h(a+b-c) = h(a)+h(b)-h(c)

amistre64 · Answer

3 operators might be a better terminology

zarkon · Answer

I can think of 2 right of the top of my head

amistre64 · Answer

i can think of 3, which is why i limited it to 3:)

zarkon · Answer

though my two can be transformed into on ...hmmm

zarkon · Answer

*one

beginnersmind · Answer

What are a, b and c? Any linear operator h fits the bill (differentiation, integration, linear transformation on any vectorspace, etc.)

amistre64 · Answer

i was thinking diff, ints, and laplace in my head;  linear transforms in general yes

amistre64 · Answer

transform is prolly a bad choice of words too lol

beginnersmind · Answer

It's actually harder to find an example for numbers, especially if you're only guessing.

It seems that all of them are 

$$h(x)=\lambda x$$

anonymous · Answer

Any ring homomorphism would work as well.

amistre64 · Answer

havent delved to far into the abstract algebra stuff yet; got number theory starting in the fall tho

anonymous · Answer

Cool :) Number Theory was very interesting.