Superposition (Linear Algebra

linear-algebra

Definition

Superposition

Superposition is forming a linear combination of elements (states/inputs) in a space with addition and scalar multiplication:

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

Equivalently:

• Additive Function:
• Homogeneity:

Principle of Superposition

If a problem/operator is linear, then linear combinations of solutions are solutions:

In the homogeneous case , any is again a solution.