Difference between revisions of "Signum"
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| − | The signum function (also called the sign function) is the function | + | The signum function $\mathrm{sgn} \colon \mathbb{R} \rightarrow \{-1,0,1\}$ (also called the sign function) is the function |
$$\mathrm{sgn}(x)=\left\{ \begin{array}{ll} | $$\mathrm{sgn}(x)=\left\{ \begin{array}{ll} | ||
| − | 1 & | + | 1, & x > 0 \\ |
| − | 0 & | + | 0, & x = 0 \\ |
| − | -1 & | + | -1, & x < 0 |
\end{array} \right.$$ | \end{array} \right.$$ | ||
| + | The function is occasionally extended to a function $\mathrm{sgn} \colon \mathbb{C} \rightarrow \mathbb{C}$ by | ||
| + | $$\mathrm{sgn}(z)=\dfrac{z}{|z|}.$$ | ||
<div align="center"> | <div align="center"> | ||
<gallery> | <gallery> | ||
| − | File:Signumplot.png|Graph of $\mathrm{sgn}$. | + | File:Signumplot.png|Graph of $\mathrm{sgn(x)}$. |
</gallery> | </gallery> | ||
</div> | </div> | ||
| + | =Properties= | ||
| + | =Videos= | ||
| + | [https://www.youtube.com/watch?v=b1xy4fVuY3U What is Signum Function in Mathematics - Learn Relations and Functions] (28 January 2013) <br /> | ||
| + | [https://www.youtube.com/watch?v=T_pGvvyjIkI Signum Function] (26 August 2016) <br /> | ||
| + | |||
| + | =References= | ||
| + | * {{BookReference|Orthogonal Polynomials|1975|Gabor Szegő|edpage = Fourth Edition|next=Signum}}: $(1.1.1)$ | ||
| + | * {{BookReference|Orthogonal Polynomials|1975|Gabor Szegő|edpage = Fourth Edition|prev=Signum|next=findme}}: $(1.1.2)$ | ||
[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
Latest revision as of 05:12, 11 February 2018
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 $$\mathrm{sgn}(z)=\dfrac{z}{|z|}.$$
Graph of $\mathrm{sgn(x)}$.
Properties
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): $(1.1.2)$
