In mathematics, a unary operation is an operation with only one operand, i.e. a single input.[1] This is in contrast to binary operations, which use two operands.[2] An example is any function , where A is a set. The function is a unary operation on A.
Common notations are prefix notation (e.g. ¬, −), postfix notation (e.g. factorial n!), functional notation (e.g. sin x or sin(x)), and superscripts (e.g. transpose AT). Other notations exist as well, for example, in the case of the square root, a horizontal bar extending the square root sign over the argument can indicate the extent of the argument.
Obtaining the absolute value of a number is a unary operation. This function is defined as where is the absolute value of .
This is used to find the negative value of a single number. Here are some examples:
For any positive integer n, the product of the integers less than or equal to n is a unary operation called factorial. In the context of complex numbers, the gamma function is an unary operation extension of factorial.
In trigonometry, the trigonometric functions, such as , , and , can be seen as unary operations. This is because it is possible to provide only one term as input for these functions and retrieve a result. By contrast, binary operations, such as addition, require two different terms to compute a result.
Below is a table summarizing common unary operators along with their symbols, description, and examples:[3]
In JavaScript, these operators are unary:[4]
++x
, x++
--x
, x--
+x
-x
~x
!x
In the C family of languages, the following operators are unary:[5][6]
++x
, x++
--x
, x--
&x
*x
+x
-x
~x
!x
sizeof x, sizeof(type-name)
(type-name) cast-expression
In the Unix shell (Bash/Bourne Shell), e.g., the following operators are unary:[7][8]
++$x
, $x++
--$x
, $x--
+$x
-$x
!$x
$x
${#x}
In the PowerShell, the following operators are unary:[9]
++$x
, $x++
--$x
, $x--
+$x
-$x
!$x
.$x
&$x
[type-name] cast-expression
+$x
,$array