# ldivide, .\

Element-wise quaternion left division

## Syntax

``C = A.\B``

## Description

example

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

## 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 0.066667 - 0.13333i - 0.2j - 0.26667k 0.057471 - 0.068966i - 0.08046j - 0.091954k ```

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

```q1 = quaternion([1:4;2:5;4:7;5:8]); A = reshape(q1,2,2)```
```A = 2x2 quaternion array 1 + 2i + 3j + 4k 4 + 5i + 6j + 7k 2 + 3i + 4j + 5k 5 + 6i + 7j + 8k ```
```q2 = quaternion(magic(4)); B = reshape(q2,2,2)```
```B = 2x2 quaternion array 16 + 2i + 3j + 13k 9 + 7i + 6j + 12k 5 + 11i + 10j + 8k 4 + 14i + 15j + 1k ```
`C = A.\B`
```C = 2x2 quaternion array 2.7 - 1.9i - 0.9j - 1.7k 1.5159 - 0.37302i - 0.15079j - 0.02381k 2.2778 + 0.46296i - 0.57407j + 0.092593k 1.2471 + 0.91379i - 0.33908j - 0.1092k ```

## Input Arguments

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Divisor, specified as a `quaternion` object, an array of `quaternion` objects of any dimensionality, a real scalar, or an array of real numbers of any dimensionality. Numeric values must be of data type `single` or `double`.

`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.

Dividend, specified as a `quaternion` object, an array of `quaternion` objects of any dimensionality, a real scalar, or an array of real numbers of any dimensionality. Numeric values must be of data type `single` or `double`.

`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.

## Output Arguments

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Result of quaternion division, returned as a `quaternion` object or an array of `quaternion` objects.

## 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,

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

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, then

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

## Version History

Introduced in R2018b