 Of course, in a classical theory, the dynamical quantities that define a state also form an algebra also, as they can be multiplied and added, and multiplied by real or complex numbers. Quantum mechanics differs from classical mechanics in that the order of multiplication of operators can make a difference.  That is, for some operators \(A\),\(B\), the product \(AB\) is not equal to the product \(BA.\) If \(AB = BA,\) the operators are said to commute.