Affine Superposition

linear-logic

Definition

Affine Superposition

Affine superposition is forming an affine combination of elements (states/inputs) in a space with addition and scalar multiplication:

(More generally: with .)

A function/system respects affine superposition (is affine linear) iff, for all and scalars with ,

Equivalently: There exists a linear map and a fixed vector such that

Principle of Affine Superposition

If a problem/operator is affine linear, then affine combinations of solutions give affine combinations of outputs:

In particular, if and , then any affine combination

is again a solution of .