Unary operation

In mathematics, a unary operation is an operation with only one operand, i.e. a single input. Specifically, it is a function

$f:\ A\to A$

where A is a set. In this case f is called a unary operation on A.

Common notations are prefix notation (e.g. +, −, not), postfix notation (e.g. factorial: n!), functional notation (e.g. sin x or sin (x)), and superscripts (e.g. transpose A^T). Other notation exists as well, for example in the case of the square root a horizontal bar over the argument extending the square root sign can indicate the extent of the argument.

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. 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)

Computer programming

Unary operators (called "monadic" in APL) are also used in programming languages.

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
• One's complement: ~x
• Logical negation: !x
• Sizeof: sizeof x, sizeof(type-name)
• Cast: (type-name) cast-expression

Other languages

Windows PowerShell

• Increment: ++$x, $x++
• Decrement: −−$x, $x−−
• Positive: +$x
• Negative: −$x
• Logical negation: -not $x
• Invoke in current scope: .$x
• Invoke in new scope: &$x
• Cast: [type-name] cast-expression

See also

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

References

• Matt Insall, "Unary Operation" from MathWorld.