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Sign function
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The sign function sgn(x), also called the signum function, of a real number is defined as
This may be compactly written as
where is the Iverson bracket.
"Sign" of complex number
The "sign" of a complex number , where is the absolute value of a complex number and is the argument of a nonzero complex number (the argument of 0 being undefined), would generalize to
The "sign" of a nonzero complex number would thus give the complex number on the unit circle of the complex plane which has the same argument as .
If we consider the real numbers as a subset of the complex numbers, then
See also
- Absolute value (abs(x))
- Heaviside step function
- {{sgn}} (mathematical function template)
- {{abs}} (mathematical function template)