# 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 the 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. 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.

## Examples

### 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 positive but it is not needed since we assume a value to be positive:

(+2) = 2

Unary positive does not change the sign of a negative operation:

(+(−2)) = (−2)

In this case a unary negative is needed to change the sign:

(−(−2)) = (+2)

### Trigonometry

In trigonometry, the trigonometric functions, such as ${\displaystyle \sin }$, ${\displaystyle \cos }$, and ${\displaystyle \tan }$, are 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 (programming language), these operators are unary:[1]

#### C family of languages

In the C family of languages, the following operators are unary:[2][3]

#### 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 it's (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