norm

Quaternion norm

Syntax

N = norm(quat)

Description

N = norm(quat) returns the quaternion's norm, quat, as the square root of the sum of its component squared.

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 $$\text{norm}(Q)=\sqrt{a^2+b^2+c^2+d^2}$$.

Examples

Calculate Quaternion Norm

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

quat — Quaternion

quaternion object | array of quaternion objects

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

Output Arguments

N — Quaternion norm

real scalar | array of real numbers

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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2020a