Unary operation

In mathematics, a unary operation is an operation with only one operand, i.e. a single input. This is in contrast to binary operations, which use two operands. An example is any function $f : A → A$, where $A$ is a set. The function $f$ is a unary operation on $A$.

Common notations are prefix notation (e.g. ¬, −), postfix notation (e.g. factorial $n!$), functional notation (e.g. $sin&thinsp;x$ 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.

Absolute value
Obtaining the absolute value of a number is a unary operation. This function is defined as $$|n| = \begin{cases} n, & \mbox{if } n\geq0 \\ -n, & \mbox{if } n<0 \end{cases}$$ where $$|n|$$ is the absolute value of $$n$$.

Negation
This is used to find the negative value of a single number. Here are some examples:


 * $$-(3) = -3$$


 * $$-( -3) = 3$$

Factorial
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.

Trigonometry
In trigonometry, the trigonometric functions, such as $$\sin$$, $$\cos$$, and $$\tan$$, 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.

Examples from programming languages
Below is a table summarizing common unary operators along with their symbols, description, and examples:

JavaScript
In JavaScript, these operators are unary:
 * Increment: ,
 * Decrement: ,
 * Positive:
 * Negative:
 * Ones' complement:
 * Logical negation:

C family of languages
In the C family of languages, the following operators are unary:


 * Increment: ,
 * Decrement: ,
 * Address:
 * Indirection:
 * Positive:
 * Negative:
 * Ones' complement:
 * Logical negation:
 * Sizeof:
 * Cast:

Unix shell (Bash)
In the Unix shell (Bash/Bourne Shell), e.g., the following operators are unary:
 * Pre and Post-Increment: ,
 * Pre and Post-Decrement: ,
 * Positive:
 * Negative:
 * Logical negation:
 * Simple expansion:
 * Complex expansion:

PowerShell
In the PowerShell, the following operators are unary:
 * Increment: ,
 * Decrement: ,
 * Positive:
 * Negative:
 * Logical negation:
 * Invoke in current scope:
 * Invoke in new scope:
 * Cast:
 * Cast:
 * Array: