3D rotation group

Definition

In mechanics and geometry, the 3D rotation group, often denoted SO(3), is the group of all rotations about the origin of three-dimensional Euclidean space under the operation of composition, which combines two rotations by performing one after the other.

Related concepts

3-sphere Absolute value Addison Wesley Adjoint representation Angle Angle of rotation Angular momentum Angular momentum operator Antipodal point Associative property Axis of rotation Axis–angle representation BCH formula Baker–Campbell–Hausdorff formula Bartel Leendert van der Waerden Basis of a vector space Bernard de Wit Bijection Bilinear transform Block diagonal matrix Boson Cartan–Dieudonné theorem Casimir element Charles P. Poole Charts on SO(3)Chirality (mathematics)Classical group Classical mechanics Classification theorem Clebsch–Gordan coefficients Clockwise and counterclockwise Closed subgroup theorem Commutation relation Commutator Compact space Computer graphics Connected space Coordinate rotation Cosmas Zachos Countably infinite Counterclockwise Course of Theoretical Physics Covering map Cross product Cyclic group David Fairlie Derivative of the exponential map Determinant Diffeomorphism Differential (mathematics)Dihedral group Dot product Elementary particle Euclidean distance Euclidean group Euclidean space Euler's rotation theorem Euler angle Euler angles Faithful representation Fermion Finite-dimensional Function composition Fundamental group General linear group Geodesic Geometric algebra Geometry Gerard 't Hooft Great circle Group (mathematics)Group homomorphism Group isomorphism Group representation Haar measure Hairy ball theorem Herbert Goldstein Hermitian matrix Hilbert–Schmidt inner product Homeomorphic Homomorphism Hypersphere of rotations Icosahedral group Ideal (Lie algebra)Identity map Identity matrix Improper rotation Infinitesimal Infinitesimal rotation Infinitesimal rotation matrix Integer Inverse function Invertible matrix Isometry Isomorphic Israel Gelfand Jordan map Kernel (algebra)Kronecker delta Kronecker product Ladder operator Law of cosines Levi-Civita symbol Lie algebra Lie algebra representation Lie bracket Lie group Linear subspace Linear transformation Lorentz group Lorentz transformation Manifold Martinus Veltman Mary L. Boas Mathematical Methods in the Physical Sciences Matrix (mathematics)Matrix exponential Matrix multiplication Matrix product Measure zero Metric signature Minkowski space Möbius transformation Nathan Jacobson Non-abelian group Nonabelian group Null space Octahedral group One-parameter subgroup Orientation (vector space)Origin (mathematics)Orthogonal Orthogonal group Orthogonal matrix Orthonormal basis Orthonormality Pauli matrices Pauli matrix Physics Pin group Plane of rotation Plate trick Quantum mechanics Quaternion Quaternions and spatial rotation Quotient space (topology)Real coordinate space Real projective space Representation of a Lie group Representation theory of SU(2)Right-hand side Rigid body Robert Adol'fovich Minlos Rodrigues' rotation formula Rotation Rotation formalisms in three dimensions Rotation matrix Rotor (mathematics)SE(3)Separable space Sign (mathematics)Simple (abstract algebra)Simply connected Skew-Hermitian matrix Skew-symmetric matrix Smooth function Smooth manifold Special orthogonal Lie algebra Special orthogonal group Special relativity Special unitary group Spherical basis Spherical harmonics Spherical law of cosines Spherical symmetry Spin(3)Spin-1/2 Spin (physics)Spin operator Spinor Spinors in three dimensions Spin–statistics theorem Standard basis Stereographic projection Structure constant Subgroup Surjective Symmetry group Tangent space Tetrahedral group Thomas Curtright Three-dimensional rotation operator Three-dimensional space Topological space Transformation (function)Transpose Turn (geometry)Unit vector Universal cover Universal covering group Universal covering space Versor

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