You have used this concept all your mathematical life. As you can see, there is nothing too cryptic at this point. But you will soon realize that this framework provides us with some powerful tools for analyzing problems. Here are some rules for working with operators. These rules define an algebra for operators.
Operators obey the associative law of multiplication, just like for numbers.
This is an extremely important point. Some operators commute with each other,while others do not. We will find that this has very important consequences for quantum mechanical operators. To investigate this property we define a new entity called the commutator of two operators. There is a special class of operators called linear operators .