# Signum

From Encyclopedia of Mathematics

The function of a real variable $x$ which is equal to $1$ if $x$ is positive, equal to 0 if $x$ is zero and equal to $-1$ if $x$ is negative. Notation: $\operatorname{sgn} x$ or $\operatorname{sign} x$. Thus,
\begin{equation*}
\operatorname{sgn} x =
\begin{cases}
\ \ \,\,1\quad \text{if } x>0,\\
\ \ \,\,0\quad \text{if } x=0,\\
-1\quad \text{if } x<0.\\
\end{cases}
\end{equation*}

#### Comments

The signum function is usually extended to the complex plane by $\operatorname{sgn} z = z / |z|$ if $z\ne0$ (and $\operatorname{sgn} 0=0$). Thus, it measures the angle of the ray from the origin on which $z$ lies.

**How to Cite This Entry:**

Signum.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Signum&oldid=28838

This article was adapted from an original article by Yu.A. Gor'kov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article