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 $f : A \to A$ , 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. $sin x$ or $sin(x)$ ), and superscripts (e.g. transpose $A T$ ). 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 where is the absolute value of .

Negation

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

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:

Technically, there is also a unary + operation but it is not needed since we assume an unsigned value to be positive:

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

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

Trigonometry

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.

Examples from programming languages

JavaScript

In JavaScript, these operators are unary:

Increment: ++x, x++
Decrement: --x, x--
Positive: +x
Negative: -x
Ones' complement: ~x
Logical negation: !x

C family of languages

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

Increment: ++x, x++
Decrement: --x, x--
Address: &x
Indirection: *x
Positive: +x
Negative: -x
Ones' complement: ~x
Logical negation: !x
Sizeof: sizeof x, sizeof(type-name)
Cast: (type-name) cast-expression

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}

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