For an abstract vector space "V" (rather than the concrete vector space formula_17), the analog of scalar matrices are scalar transformations. This is true more generally for a module "M" over a ring "R", with the endomorphism algebra End("M") (algebra of linear operators on "M") replacing the algebra of matrices. Formally, scalar multiplication is a linear map, inducing a map formula_18 (from a scalar "λ" to its corresponding scalar transformation, multiplication by "λ") exhibiting End("M") as a "R"-algebra. For vector spaces, the scalar transforms are exactly the center of the endomorphism algebra, and, similarly, invertible transforms are the center of the general linear group GL("V"). The former is more generally true free modules formula_19, for which the endomorphism algebra is isomorphic to a matrix algebra.