The composite matrix in a composite material is its continuous surrounding phase, distinguished from embedded fibres or particles. It holds the reinforcement together and transfers load through interfacial stresses; it can also protect the reinforcement from damage or the environment.
For a fibre-reinforced polymer, the polymer is the composite matrix even if the fibres carry much of the axial load. Matrix stiffness, interfacial adhesion and failure therefore affect the whole specimen. This materials meaning differs from a rectangular array of numbers in linear algebra.
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