Affine-linear mapping/Functorial properties/Fact

Let be a field, and let and denote affine spaces over the vector spaces  and . Then the following statements hold.

  1. The identity

    is affine-linear.

  2. The composition of affine-linear mappings

    and

    is again affine-linear.

  3. For a bijective affine-linear mapping

    also the inverse mapping is affine-linear.

  4. For , the translation

    is affine-linear.

  5. A linear mapping is affine-linear.