Difference between revisions of "Signum"

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

Properties

Videos

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

References