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The signum function is the real valued function defined for real as follows
For all real we have
. Similarly,
. If
then also
. The second property implies that for real non-zero
we have
.
For a complex argument it is defined by
where denotes the magnitude (absolute value) of
. In other words, the signum function project a non-zero complex number to the unit circle
.
We have , where
is the complex conjugate of
.
Cite this web-page as:
Štefan Porubský: Signum Function.