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# rdivide, ./

Element-wise quaternion right division

Since R2018b

## Description

example

C = A./B performs quaternion element-wise division by dividing each element of quaternion A by the corresponding element of quaternion B.

## Examples

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Create a 2-by-1 quaternion array, and divide it element-by-element by a real scalar.

A = quaternion([1:4;5:8])
A = 2x1 quaternion array
1 + 2i + 3j + 4k
5 + 6i + 7j + 8k

B = 2;
C = A./B
C = 2x1 quaternion array
0.5 +   1i + 1.5j +   2k
2.5 +   3i + 3.5j +   4k

Create a 2-by-2 quaternion array, and divide it element-by-element by another 2-by-2 quaternion array.

q1 = quaternion(magic(4));
A = reshape(q1,2,2)
A = 2x2 quaternion array
16 +  2i +  3j + 13k      9 +  7i +  6j + 12k
5 + 11i + 10j +  8k      4 + 14i + 15j +  1k

q2 = quaternion([1:4;3:6;2:5;4:7]);
B = reshape(q2,2,2)
B = 2x2 quaternion array
1 + 2i + 3j + 4k     2 + 3i + 4j + 5k
3 + 4i + 5j + 6k     4 + 5i + 6j + 7k

C = A./B
C = 2x2 quaternion array
2.7 -      0.1i -      2.1j -      1.7k       2.2778 + 0.092593i -  0.46296j -  0.57407k
1.8256 - 0.081395i +  0.45349j -  0.24419k       1.4524 -      0.5i +   1.0238j -   0.2619k

## Input Arguments

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Dividend, specified as a quaternion, an array of quaternions, a real scalar, or an array of real numbers.

A and B must have compatible sizes. In the simplest cases, they can be the same size or one can be a scalar. Two inputs have compatible sizes if, for every dimension, the dimension sizes of the inputs are the same or one of the dimensions is 1.

Data Types: quaternion | single | double

Divisor, specified as a quaternion, an array of quaternions, a real scalar, or an array of real numbers.

A and B must have compatible sizes. In the simplest cases, they can be the same size or one can be a scalar. Two inputs have compatible sizes if, for every dimension, the dimension sizes of the inputs are the same or one of the dimensions is 1.

Data Types: quaternion | single | double

## Output Arguments

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Result of quaternion division, returned as a scalar, vector, matrix, or multidimensional array.

Data Types: quaternion

## Algorithms

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### Quaternion Division

Given a quaternion $A={a}_{1}+{a}_{2}\text{i}+{a}_{3}\text{j}+{a}_{4}\text{k}$ and a real scalar p,

$C=A./p=\frac{{a}_{1}}{p}+\frac{{a}_{2}}{p}\text{i}+\frac{{a}_{3}}{p}\text{j}+\frac{{a}_{4}}{p}\text{k}$

Note

For a real scalar p, A./p = A.\p.

### Quaternion Division by a Quaternion Scalar

Given two quaternions A and B of compatible sizes,

$C=A./B=A.*{B}^{-1}=A.*\left(\frac{conj\left(B\right)}{norm{\left(B\right)}^{2}}\right)$

## Version History

Introduced in R2018b