Unary operation

Short description: Mathematical operation with only one operand

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 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 [math]\displaystyle{ |n| = \begin{cases} n, & \mbox{if } n\geq0 \\ -n, & \mbox{if } n\lt 0 \end{cases} }[/math] where [math]\displaystyle{ |n| }[/math] is the absolute value of [math]\displaystyle{ n }[/math].

Negation

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

[math]\displaystyle{ -(3) = -3 }[/math]

[math]\displaystyle{ -( -3) = 3 }[/math]

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:

[math]\displaystyle{ 3 }[/math][math]\displaystyle{ - }[/math][math]\displaystyle{ - }[/math][math]\displaystyle{ 2 }[/math]

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:

[math]\displaystyle{ 3 }[/math][math]\displaystyle{ - }[/math][math]\displaystyle{ (- }[/math][math]\displaystyle{ 2) }[/math][math]\displaystyle{ = 5 }[/math]

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

[math]\displaystyle{ +2 = 2 }[/math]

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

[math]\displaystyle{ + }[/math][math]\displaystyle{ (- }[/math][math]\displaystyle{ 2) }[/math][math]\displaystyle{ = }[/math] [math]\displaystyle{ -2 }[/math]

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

[math]\displaystyle{ -(-2)=+2 }[/math]

Trigonometry

In trigonometry, the trigonometric functions, such as [math]\displaystyle{ \sin }[/math], [math]\displaystyle{ \cos }[/math], and [math]\displaystyle{ \tan }[/math], 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

See also

• Binary operation
• Iterated binary operation
• Ternary operation
• Arity
• Operation (mathematics)
• Operator (programming)