What Is a Rotation Matrix?

A rotation matrix is a matrix used to rotate an axis about a given point. The center of a Cartesian coordinate frame is typically used as that point of rotation. Rotation matrices are used for computations in aerospace, image processing, and other technical computing applications.

The revolution of a rotation matrix is often described with Euler angles, but can also be described in vector form using quaternions. Although there are many methods to perform a rotation, the most prevalent are based on directional cosine matrices and quaternions.

Common tasks include::

Performing 2D and 3D rotations using a single function call
Converting between quaternion vectors and rotation matrices
Actively using matrix operations for rotation in simulation

For details on implementing a rotation matix, see MATLAB^® and Simulink^®.

Examples and How To

Rotate an Image - Example
Use Group Objects to Apply a Rotation Matrix - Example
Representations of Body Orientation in Simscape Multibody - Example

Software Reference

Aerospace Toolbox - Overview
Convert Rotation Angle to Quaternion - Function
Rotation Angles to Direction Cosine Matrix - Block
Create 4-by-4 Transform Matrix - Function

What Is Aerospace Toolbox?

What Is Aerospace Blockset?

Fly a 747 with MATLAB