# norm

Quaternion norm

## 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 scalar, vector, matrix, or multidimensional array of quaternions.

Data Types: quaternion

## Output Arguments

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Quaternion norm. If the input quat is an array, the output is returned as an array the same size as quat. Elements of the array are real numbers with the same data type as the underlying data type of the quaternion, quat.

Data Types: single | double

## Extended Capabilities

### Topics

Introduced in R2018b