úÎHVNoneNote:  in the  instance operates under  intersection . i.e.: P(MapVector $ Map.fromList [("x", id)]) <*> (MapVector $ Map.fromList [("y", 3)])MapVector (Map.fromList []) in the J instance performs elementwise multiplication. It is defined in terms of  1 and therefore also operates under intersection: `(MapVector $ Map.fromList [("x", 2), ("y", 3)]) * (MapVector $ Map.fromList [("x", 5),("y", 7)])/MapVector (Map.fromList [("x", 10), ("y", 21)])W(MapVector $ Map.fromList [("x", 2), ("y", 3)]) * (MapVector $ Map.fromList [("y", 7)])$MapVector (Map.fromList [("y", 21)]) in the G instance multiplies by the scalar of v. Nesting MapVectors preserves  the scalar type, e.g.  Scalar (MapVector k (MapVector k' v)) = Scalar v. I2 *^ (ConstantMap $ MapVector $ Map.fromList [("x", 3 :: Int), ("y", 5)])5ConstantMap (MapVector (fromList [("x",6),("y",10)])) Finally,   in  F is the dot-product operator. Again, it operates under intersection. i(MapVector $ Map.fromList [("x", 2 :: Int), ("y", 3)]) <.> (MapVector $ Map.fromList [("x", 5),("y", 7)])31s(pure . MapVector $ Map.fromList [("x", 2 :: Int), ("y", 3)]) <.> (MapVector $ Map.fromList [("a", pure (5::Int))])25Addition, using either   or  , operates under union. EAn infinite-dimensional vector with the same value on all dimensions        vector-space-map-0.1.0.1Data.Map.Vector MapVector ConstantMapbaseControl.Applicative<*> ApplicativeGHC.Num*Numvector-space-0.8.6Data.VectorSpace*^ VectorSpace<.> InnerSpace+Data.AdditiveGroup^+^$fNumMapVector$fInnerSpaceMapVector$fVectorSpaceMapVector$fAdditiveGroupMapVector$fApplicativeMapVector