In mathematics, “operator” has two main definitions. 1) An operator is a mathematical symbol, for example **+**, that represents an operation or action. In this case, the operator **+** says to add. The entire mathematical statement might be: **2 + 3**. The operator **+ **says: add **2** and **3**. Other familiar operators are **– **(subtract) and **X **(multiply).

**Operator in calculus.** In calculus, **d/dx **is an operator that says to find the derivative of a function. For example, **d/dx f(x)** means to find the derivative of the function **f(x)**. Calculus includes other operators as well.

2) **Operator in vector mathematics.* **In vector mathematics, an operator is a mathematical expression that says to take one vector and manipulate it so as to create another vector of a particular kind. This is also called “mapping” one vector to another. An operator or “mapping” is like a mathematical function: feed it one vector as an input, and, then, output another vector. This type of operator can be used by physicists to describe how one physical state, represented by a vector, becomes another, represented by another vector.

*Vector mathematics is also called “linear algebra.” While arithmetic manipulates individual numbers (3, 1017, etc.), vector math manipulates groups of numbers, for example the two-number group ⟨0, 1⟩ or the three-number group ⟨1,0,3⟩.