Question

Hello, can someone please explain me about commutation? I think there are two main types of calculating methods: classical and operational. Can you please explain how they're done.?

Answer 1

There's not really a distinction like that. Mathematical objects that have a well-defined multiplication operation (or something like that) can either commute or not. C-numbers (your typical complex numbers) commute, matrices in general do not. Other general structures (operators) could be defined however you like.

Can you clarify your question? The computations don't change, you just aren't allowed to freely change the order of multiplication.

Answer 2

hint:
when you compute a commutator operator, you have to specify the quantities involved in such commutator. For example the commutator between two matrices /real or complex), in general, is different from zero, whereas the commutator, between two scalar qauntities or between two real function is always equal to zero.
Please refer to my subsequent tutorial:
http://openstudy.com/study#/updates/561d1b1fe4b0cadb1e103c5e

Answer 3

Ah, I see. I know what a commutator is in that sense, but I'm not familiar with the terminology "classical vs. operational" as it applies to one. Can you elaborate a bit more?