# norm

Quaternion norm

Since R2020a

## Description

example

N = norm(quat) returns the norm of the quaternion, quat.

Given a quaternion of the form $Q=a+b\text{i}+c\text{j}+d\text{k}$, the norm of the quaternion is defined as $\text{norm}\left(Q\right)=\sqrt{{a}^{2}+{b}^{2}+{c}^{2}+{d}^{2}}$.

## Examples

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Create a scalar quaternion and calculate its norm.

quat = quaternion(1,2,3,4);
norm(quat)
ans = 5.4772

The quaternion norm is defined as the square root of the sum of the quaternion parts squared. Calculate the quaternion norm explicitly to verify the result of the norm function.

[a,b,c,d] = parts(quat);
sqrt(a^2+b^2+c^2+d^2)
ans = 5.4772

## Input Arguments

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Quaternion for which to calculate the norm, specified as a quaternion object or an array of quaternion objects of any dimensionality.

## Output Arguments

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Quaternion norm, returned as a real scalar or an array of real numbers of the same size as the quat argument. Elements of N are of the same data type as the underlying data type of quat.

Data Types: single | double

## Version History

Introduced in R2020a