The elementary arithmetic operators
- addition symbolized by '+'
- subtraction symbolized by '-'
- multiplication symbolized by '*' or by simple juxtaposition.
- division symbolized by '/', '÷' or a horizontal line separating numerator from denominator
- exponentiation (repeated multiplication) by elevation of the number of factors above the base line
are quite standard.
Different branches of mathematics may extend the definitions of operators to represent analogous operations.
- The concept of an addition operator '+' has been extended to cover addition of sets, vectors and matrices.
- Multiplication of a vector by a particular matrix is a unary operator or transformation; it is common, and only a slight abuse of language, to say the matrix is the operator.