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Orthogonal transformationSubrepresentationLinear mapTensor algebraTopological propertyTranspose of a linear mapProjectionLinear subspaceInvariant measureSelf-adjoint operatorIndicator vectorSubspace topologyLinear spanDual spaceBilinear formAffine groupIsometryMapping class groupSubmanifoldTopological vector spaceTensor productIsometry groupBounded operatorSymmetric bilinear formContinuous linear operatorOrthonormal basisSubbundleInvariant manifoldOrthogonal groupMeasurable functionMultilinear formIndefinite orthogonal groupGeometric transformationEquivariant mapSymplectic vector spaceRigid transformationNormal subgroupLinear algebraic groupInvariantComplemented subspaceEuclidean groupExact coverHolomorphic vector bundleOrthogonal basisCorrespondenceDual basisPositive linear functionalInclusion mapBilinear mapCategory of topological spacesCovariantTransversalityCovering groupAdjoint representationLinear transformationLie algebraConnectorTautological bundleDualEigenspaceOrthogonal matrixRelatively compact subspaceAutomorphism groupProjective geometryEuclidean plane isometryCharacteristic polynomialLinear independenceContravariantSymmetric spaceOrthogonal functionsEigenvalueLinear functionalOrthogonalizationHomeomorphismDistributionDimensionExponential mapSymplectomorphismHermitian adjointProjection-valued measureFlatOrthogonal complementBandQuasiconvex functionTraceIdealRegular representationRotational invarianceEuclidean topologyCompact operatorGroup actionDegenerate bilinear formLattice of subgroupsMatrix normMorphismSymmetric algebraCotangent bundleConformal groupProjective linear groupEigenfunction