In mathematics, an 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 : AA, 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. sinx 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.

## Examples

### Absolute Value

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

### Negation

This is used to find the negative value of a single number. This is technically not a unary operation as $-n$ is just short form of $0-n$ . Here are some examples:

$-(3)=-3$ $-(-3)=3$ ### Unary negative and positive

As unary operations have only one operand they are evaluated before other operations containing them. Here is an example using negation:

$3$ $-$ $-$ $2$ Here, the first '−' represents the binary subtraction operation, while the second '−' represents the unary negation of the 2 (or '−2' could be taken to mean the integer −2). Therefore, the expression is equal to:

$3$ $-$ $(-$ $2)$ $=5$ Technically, there is also a unary + operation but it is not needed since we assume an unsigned value to be positive:

$+2=2$ The unary + operation does not change the sign of a negative operation:

$+$ $(-$ $2)$ $=$ $-2$ In this case, a unary negation is needed to change the sign:

$-(-2)=+2$ ### 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

#### JavaScript

In JavaScript, these operators are unary:

#### C family of languages

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

#### Unix Shell (Bash)

In the Unix/Linux shell (bash/sh), '$' is a unary operator when used for parameter expansion, replacing the name of a variable by its (sometimes modified) value. For example: • Simple expansion: $x
• Complex expansion: ${#x} #### Windows PowerShell • Increment: ++$x, $x++ • Decrement: −−$x, $x−− • Positive: +$x
• Negative: −$x • Logical negation: !$x
• Invoke in current scope: .$x • Invoke in new scope: &$x
• Cast: [type-name] cast-expression
• Cast: +$x • Array: ,$array

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