Example image of eyePlorer eyePlorer map for 'Rotation group': Orthogonal group Classical mechanics Euclidean space Function composition Geometry Group (mathematics) Rotation Euclidean vector Isometry Length Linear map Orientation (mathematics) Improper rotation Reflection (mathematics) Identity function Lie group Manifold Smooth function Angle Dot product Orthonormal basis Dimension (vector space) Matrix (mathematics) Standard basis Identity matrix Transpose Orthogonal matrix Determinant Subgroup Isomorphism Matrix multiplication General linear group Invertible matrix Nonabelian group Cartan–Dieudonné theorem Euclidean subspace Euler's rotation theorem Orthogonality Clockwise Unit vector Up to Antipodal point Quotient space Homeomorphism Topological space Diffeomorphism Differentiable manifold Real projective space Connectedness Simply connected space