 Student[MultivariateCalculus] - Maple Programming Help

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Student[MultivariateCalculus]

 Normalize

 Calling Sequence Normalize(a, p)

Parameters

 a - Vector with algebraic entries p - (optional) a real number greater than or equal to $1$, infinity, or Euclidean; defaults to $2$

Description

 • The Normalize command computes a normalized by the p-norm.
 • If p is set to Euclidean, then the $2$-norm is used.
 • Let $\left|\left|a\right|\right|$ denote the p-norm or infinity norm. Then a normalized is given by $\frac{a}{\left|\left|a\right|\right|}$.

Examples

 > $\mathrm{with}\left(\mathrm{Student}:-\mathrm{MultivariateCalculus}\right):$
 > $v≔⟨1,2,3⟩$
 ${v}{≔}\left[\begin{array}{c}{1}\\ {2}\\ {3}\end{array}\right]$ (1)
 > $\mathrm{Normalize}\left(v\right)$
 $\left[\begin{array}{c}\frac{\sqrt{{14}}}{{14}}\\ \frac{\sqrt{{14}}}{{7}}\\ \frac{{3}{}\sqrt{{14}}}{{14}}\end{array}\right]$ (2)
 > $\mathrm{Normalize}\left(v,\mathrm{\infty }\right)$
 $\left[\begin{array}{c}\frac{{1}}{{3}}\\ \frac{{2}}{{3}}\\ {1}\end{array}\right]$ (3)
 > $\mathrm{Normalize}\left(v,1\right)$
 $\left[\begin{array}{c}\frac{{1}}{{6}}\\ \frac{{1}}{{3}}\\ \frac{{1}}{{2}}\end{array}\right]$ (4)

Compatibility

 • The Student[MultivariateCalculus][Normalize] command was introduced in Maple 2016.