Signum

The signum function $\mathrm{sgn} \colon \mathbb{R} \rightarrow \{-1,0,1\}$ (also called the sign function) is the function $$\mathrm{sgn}(x)=\left\{ \begin{array}{ll} 1, & x > 0 \\ 0, & x = 0 \\ -1, & x < 0 \end{array} \right.$$ The function is occasionally extended to a function $\mathrm{sgn} \colon \mathbb{C} \rightarrow \mathbb{C}$ by $$\mathrm{sgn}(z)=\dfrac{z}{|z|}.$$

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  Graph of $\mathrm{sgn(x)}$.

Videos

What is Signum Function in Mathematics - Learn Relations and Functions (28 January 2013)
Signum Function (26 August 2016)

References

• 1975: Gabor Szegő: Orthogonal Polynomials ... (next): $(1.1.1)$
• 1975: Gabor Szegő: Orthogonal Polynomials ... (previous) ... (next): $(1.1.2)$