# quat2dcm

Convert quaternion to direction cosine matrix

## Syntax

```n = quat2dcm(q) ```

## Description

`n = quat2dcm(q)` calculates the direction cosine matrix, `n`, for a given quaternion, `q`. Input `q` is an `m`-by-4 matrix containing `m` quaternions. `n` returns a 3-by-3-by-`m` matrix of direction cosine matrices. The direction cosine matrix performs the coordinate transformation of a vector in inertial axes to a vector in body axes. Each element of `q` must be a real number.

Aerospace Toolbox uses quaternions that are defined using the scalar-first convention. This function normalizes all quaternion inputs.

## Examples

Determine the direction cosine matrix from ```q = [1 0 1 0]```:

```dcm = quat2dcm([1 0 1 0]) dcm = 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(:,:,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``` 