The Normalize(V) function returns a Vector in which each component of V has been divided by the infinity-norm for V.

An alternate norm may be selected by using the Normalize(V, p) form of the calling sequence.

The inplace option (ip) determines where the result is returned.  If given as inplace=true, the result overwrites the first argument.  Otherwise, if given as inplace=false or if this option is not included in the calling sequence, the result is returned in a new Vector.

The condition inplace=true can be abbreviated to inplace.

The inplace option must be used with caution since, if the operation fails, the original Vector argument may be corrupted.

The conjugate option (conj) determines whether complex conjugates are used when computing the norm of the input Vector, V. Note that the form conjugate=false has an effect only if a norm selection parameter is also given which specifies an even power norm (for example, Normalize(V, 2, conjugate=false).

The constructor options provide additional information (readonly, shape, storage, order, datatype, and attributes) to the Vector constructor that builds the result. These options may also be provided in the form outputoptions=[...], where [...] represents a Maple list.  If a constructor option is provided in both the calling sequence directly and in an outputoptions option, the latter takes precedence (regardless of the order).

The inplace and constructor options are mutually exclusive.

This function is part of the LinearAlgebra package, and so it can be used in the form Normalize(..) only after executing the command with(LinearAlgebra). However, it can always be accessed through the long form of the command by using LinearAlgebra[Normalize](..).

$\mathrm{with}\left(\mathrm{LinearAlgebra}\right)\:$

$\mathrm{Normalize}\left(⟨3\,0\,4⟩\,\mathrm{Euclidean}\right)$

$\left[\begin{array}{c}\frac{3}{5}\\ 0\\ \frac{4}{5}\end{array}\right]$

$V≔⟨1.55\left|1.56\right|1.53⟩$

$V≔\left[\begin{array}{ccc}1.55& 1.56& 1.53\end{array}\right]$

$\mathrm{Normalize}\left(V\,\mathrm{inplace}\right)$

$\left[\begin{array}{ccc}0.9935897436& 1.000000000& 0.9807692307\end{array}\right]$

$V$

$\left[\begin{array}{ccc}0.9935897436& 1.000000000& 0.9807692307\end{array}\right]$

$\mathrm{Normalize}\left(⟨a\,b\,c⟩\,\mathrm{Euclidean}\,\mathrm{conjugate}=\mathrm{false}\right)$

$\left[\begin{array}{c}\frac{a}{\sqrt{a^2+b^2+c^2}}\\ \frac{b}{\sqrt{a^2+b^2+c^2}}\\ \frac{c}{\sqrt{a^2+b^2+c^2}}\end{array}\right]$