Superposition Principle

The superposition principle states that for a linear system, the response to two or more combined stimuli equals the sum of the responses each stimulus would produce on its own: if input A produces response X and input B produces response Y, then input A plus B produces response X plus Y. A function satisfying this is called linear, and the principle reduces to two simpler properties, additivity and homogeneity under scalar multiplication. It applies to any linear system, including algebraic equations, linear differential equations, and systems of equations of those forms, and explains why linear systems are comparatively easy to analyze mathematically.