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 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.

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)

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

Unix Shell (Bash)

In the Unix/Linux shell (bash/sh), '$' is a unary operator, used for parameter expansion, replacing the name of a variable by its (sometimes modified) value. For example:

• Simple expansion: $x
• Complex expansion: ${#x}
• Command substitution: $(cmd)
• Arithmetic expansion: $((expr))

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", MathWorld.