In mathematics, a linear map or linear function f(x) is a function that satisfies the two properties:[1]

  • Additivity [Additivity]: f(x + y) = f(x) + f(y).
  • Homogeneity [Homogeneity] of degree 1: f(αx) = α f(x) for all α.

These properties are known as the superposition principle. In this definition, x is not necessarily a real number, but can in general be an element of any vector space.

(“Linearity” 2022)