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linalg::normalize

Normalize a vector

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Syntax

linalg::normalize(v)

Description

linalg::normalize(v) normalizes the vector with respect to the 2-norm ( ).

The result of linalg::normalize(v) is a vector that has norm 1 and the same direction as v.

The scalar product for a vector is implemented by the function linalg::scalarProduct.

The norm of a vector is computed with the function norm, which is overloaded for vectors. See the method "norm" of the domain constructor Dom::Matrix for details.

If the norm is an object that cannot be converted into an element of the component ring of v, then an error occurs (see Example 2).

Examples

Example 1

We define the following vector:

u := matrix([[1, 2]])

Then the vector of norm 1 with the same direction as u is given by:

linalg::normalize(u)

Example 2

The following computation fails because the vector (1, 2) cannot be normalized over the rationals:

v := Dom::Matrix(Dom::Rational)([[1, 2]]):
linalg::normalize(v)
Error: Cannot normalize the given vector over its component ring. [linalg::normalize]

If we define v over the real numbers, then we get the normalized vector of v as follows:

w := Dom::Matrix(Dom::Real)(v): linalg::normalize(w)

Parameters

v

A vector, i.e., an n×1 or 1 ×n matrix of a domain of category Cat::Matrix

Return Values

Vector of the same domain type as v.

See Also

MuPAD Functions

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