# exp

Exponential of quaternion array

## Syntax

``B = exp(A)``

## Description

example

````B = exp(A)` computes the exponential of the elements of the quaternion array `A`.```

## Examples

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Create a 4-by-1 quaternion array A.

`A = quaternion(magic(4))`
```A=4×1 quaternion array 16 + 2i + 3j + 13k 5 + 11i + 10j + 8k 9 + 7i + 6j + 12k 4 + 14i + 15j + 1k ```

Compute the exponential of A.

`B = exp(A)`
```B=4×1 quaternion array 5.3525e+06 + 1.0516e+06i + 1.5774e+06j + 6.8352e+06k -57.359 - 89.189i - 81.081j - 64.865k -6799.1 + 2039.1i + 1747.8j + 3495.6k -6.66 + 36.931i + 39.569j + 2.6379k ```

## Input Arguments

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Input quaternion, specified as a scalar, vector, matrix, or multidimensional array.

Data Types: `quaternion`

## Output Arguments

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

Data Types: `quaternion`

## Algorithms

Given a quaternion $A=a+b\text{i}+c\text{j}+d\text{k}=a+\overline{v}$, the exponential is computed by

`$\mathrm{exp}\left(A\right)={e}^{a}\left(\mathrm{cos}‖\overline{v}‖+\frac{\overline{v}}{‖\overline{v}‖}\mathrm{sin}‖\overline{v}‖\right)$`

## Extended Capabilities

### Topics

Introduced in R2018b