Modularity is essential for automatic composition of real software systems from ready-made components. But given ready-made components do not necessarily correspond exactly to the units and functionality of designed software system architecture modules. One needs a neat composition procedure that guarantees the necessary and sufficient components to provide required units. Linear Software Models are rigorous theoretical standards subsuming modularity. The Linear-Reducible model is proposed as a model of wellcomposed software systems, above and beyond software variability. Indeed, case studies of representative systems recognized as well-composed, be they small, intermediate building blocks or large scale, are shown to be Linear-Reducible. The paper lays down theoretical foundationsupon exact linear independence and reducible matrix conceptsproviding new precise meanings to familiar modularity ideas, such as the single responsibility theorem. The theory uses a Modularity Matrixlinking independent software structors to composable software functionals in a Linear Model. 92 Exman I..