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The 28 pages that link to Rotation matrix, each with the reason it gives.

• Angular velocityCompared with: It encodes a finite orientation change, unlike angular velocity's instantaneous rate.

• Rigid bodyRelated: It represents orientation while preserving lengths and angles.

• Linear mapBroader topic: Rotations give concrete geometric examples of linear maps that preserve lengths and angles.

• Linear operatorBroader topic: It is a familiar geometric example of a linear operator.

• Axis of rotationRelated: Its entries can encode a rotation around a specified axis.

• Rigid body dynamicsRelated: It maps body-fixed vectors into an inertial frame without changing their geometry.

• EigenvectorCompared with: A nontrivial planar rotation has no real eigenvector, despite preserving lengths.

• Orthogonal matrixBroader topic: Proper rotations are orthogonal matrices with determinant 1.

• Ecliptic coordinate systemRelated: A rotation about the equinox axis implements the basic frame conversion.

• Euler anglesRelated: Successive Euler rotations can be composed by multiplying their rotation matrices.

• Complex multiplicationRelated: Multiplication by a unit complex number represents the same planar rotation.

• Imaginary unitRelated: Multiplication by i acts on the complex plane as a 90-degree rotation.

• Angular displacementRelated: Finite changes in orientation can be represented by composing rotation matrices.

• Geometric algebraCompared with: Rotors represent rotations through algebraic multiplication rather than matrix action.

• OrientationRelated: It maps an object's axes into a reference frame and composes orientations through matrix multiplication.

• Polar formCompared with: Multiplication by a unit complex number gives the same planar rotation more compactly.

• Robot kinematicsRelated: It represents the orientation component of a link or end-effector pose.

• Vector (physics)Related: It changes vector components between rotated frames without changing the physical vector.

• Moiré patternRelated: Relative rotation changes the orientation and spacing of moiré fringes.

• Rotation (geometry)Related: Multiplying coordinates by it computes a planar rotation.

• Directed angleRelated: Its signed parameter encodes the same oriented planar rotation as a directed angle.

• Rotation groupRelated: Matrices provide a concrete way to calculate and compose rotations.

• Crystallographic restriction theoremRelated: The theorem identifies which rotation matrices can also preserve a periodic lattice.

• Euler's rotation theoremRelated: A proper rotation is represented by an orthogonal matrix with determinant one.

• Chasles' theoremRelated: The rotational part of a displacement matrix determines the screw axis direction.

• Imaginary numberRelated: Multiplication by i acts as a 90-degree rotation in the complex plane.

• Jacobian matrix and determinantBroader topic: Its determinant is one, showing that rotation preserves oriented volume.

• Rotations in 4-dimensional Euclidean spaceRelated: It is the coordinate representation used to distinguish these rotations from broader rigid motions.