Can anyone explain to me what commutators are, and what they are useful for?

Question

anonymous · Answer

They help to provide energy to a motor. It is a form of generator

snowfire · Answer

Are you sure you're talking about the same kind of commutator? For example, if A and B commute, then AB=BA

anonymous · Answer

i uses the distributive property or is very close to it

snowfire · Answer

I still don't think it's a basic property of math. I think it has to do with [A, B], but I don't what or how it's related.

schrodingers_cat · Answer

The commuter of two matrices is defined as 

[A,B] = AB -BA

As, such if this value is zero then the two matrices commute. This is used extensively in quantum mechanics for example Heisenberg uncertainty principal states that operators representing observables don't commute. Also, you can use this definition to show that the the commuter between two Pauli spin matrices is equal to a factor times the the third spin matrix.

Hope this helps :)

schrodingers_cat · Answer

Oops it should be some observables*