# quat2dcm

Convert quaternion to direction cosine matrix

## Syntax

``dcm = quat2dcm(q)``

## Description

example

````dcm = quat2dcm(q)` calculates the direction cosine matrix, `n`, for a given quaternion, `q`. Aerospace Toolbox uses quaternions that are defined using the scalar-first convention. This function normalizes all quaternion inputs.```

## Examples

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Determine the direction cosine matrix from the single quaternion q = [1 0 1 0].

`dcm = quat2dcm([1 0 1 0])`
```dcm = 3×3 0 0 -1.0000 0 1.0000 0 1.0000 0 0 ```

Determine the direction cosine matrices from multiple quaternions.

```q = [1 0 1 0; 1 0.5 0.3 0.1]; dcm = quat2dcm(q)```
```dcm = dcm(:,:,1) = 0 0 -1.0000 0 1.0000 0 1.0000 0 0 dcm(:,:,2) = 0.8519 0.3704 -0.3704 0.0741 0.6148 0.7852 0.5185 -0.6963 0.4963 ```

## Input Arguments

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Quaternion, specified as an m-by-4 matrix containing m quaternions. Each element of q must be a real number.

Data Types: `double`

## Output Arguments

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Direction cosine matrices, returned as a 3-by-3-by-m matrix, where m is the number of direction cosine matrices. The direction cosine matrix performs the coordinate transformation of a vector in inertial axes to a vector in body axes.

## Version History

Introduced in R2006b