EntityQ1783179· pop 22· linked from 550 articlesorthogonal groupSign in to savemathematical group consisting of transformations of a Euclidean space which preserve distance and a fixed pointConnectionsgroup actionEntityEuclidean spaceEntityquadratic formEntityintegerEntitysimilarityEntityhomothetic transformationEntityLie groupEntitycyclic groupEntityconnected spaceEntityorthogonal matrixEntityreflectionEntitytopological groupEntitycenterEntityCoxeter groupEntitycovering spaceEntityrotation group SO(3)Entityup toEntitymultiplicative groupEntitymathematicsEntityInternational Standard Book NumberEntityCategoriesEuclidean symmetriesLie groupsLinear algebraic groupsQuadratic forms