Rotation Matrix

A 3×3 orthogonal matrix with determinant +1 that represents the orientation of one coordinate frame relative to another. Rotation matrices compose by multiplication (R_total = R2 · R1), are always invertible (R⁻¹ = Rᵀ), and preserve vector lengths. They form the Special Orthogonal group SO(3). In robotics, rotation matrices are the core building block of homogeneous transformations.