Rotation matrix

A rotation matrix is a square matrix that rotates vectors while preserving lengths and angles. Its columns are orthonormal, and its determinant is 1.

Orthogonal matrix: A square matrix whose transpose is its inverse, so it preserves Euclidean lengths and angles. Every rotation matrix is orthogonal, but orthogonal matrices may also include reflections.
Linear transformation: A function between vector spaces that preserves vector addition and scalar multiplication. A rotation matrix is a coordinate representation of a linear transformation.
Computer graphics: The field of creating and manipulating images with computers. Graphics pipelines use rotation matrices to orient objects and cameras.
Reflection matrix: A matrix representing a reflection, which reverses orientation while preserving lengths and angles. It is orthogonal like a rotation matrix, but has determinant −1.
Special orthogonal group: The group of real orthogonal matrices with determinant 1. Rotation matrices in a fixed dimension form this group under matrix multiplication.
Matrix multiplication: An operation that composes matrices when their dimensions are compatible. Multiplying rotation matrices combines rotations, generally in an order-sensitive way.
Robotics: The engineering field concerned with designing and controlling robots. Robots use rotation matrices to track orientations of links, tools, and sensors.
Quaternion: A four-component number system used to represent three-dimensional rotations. Quaternions avoid some parameter singularities and interpolation problems of matrix-based orientation.
Determinant: A scalar associated with a square matrix that describes signed volume scaling. A determinant of 1 distinguishes rotations from reflections among orthogonal transformations.
Transpose: The matrix formed by exchanging a matrix's rows and columns. For a rotation matrix, the transpose is its inverse and undoes the rotation.

Linked from 28 pages