the matrix phase
A composite is two materials working as a team. The matrix is the continuous background material that surrounds and glues everything else together, like the mud in a mud-and-straw brick or the concrete around steel bars. If you sliced a composite open, the reinforcement would sit inside the matrix like raisins in a loaf, and the loaf itself is the matrix.
The matrix has three jobs: it binds the reinforcement in place, it transfers applied load into the reinforcement through the interface (shear along the reinforcement surfaces), and it protects the reinforcement from scratches, moisture, and abrasion. It is usually the softer, lower-stiffness, tougher partner. For example, in carbon-fiber reinforced polymer (CFRP) the matrix is an epoxy of modulus about 3 GPa, while the carbon fibers are about 230 GPa; the epoxy alone would carry almost no load, but it feeds stress into the fibers and stops one broken fiber from unloading the whole part.
Matrix choice defines the composite's family and its ceiling: polymer matrices are light and cheap but soften above roughly 150 to 250 degrees C; metal matrices tolerate more heat and conduct; ceramic matrices survive extreme heat but stay brittle. The matrix usually sets the transverse strength, the maximum service temperature, and the resistance to environment, so a carbon-fiber part often fails not in the fibers but in the matrix or at the interface.
In a fiberglass boat hull, the glassy polyester resin is the matrix; it holds the glass fibers in a shape and keeps water out, while the fibers carry the bending loads of the waves.
The matrix is the continuous phase; the reinforcement is dispersed within it.
The matrix is rarely the strong part. Its job is to hold, protect, and transfer load, not to be the load-bearing star, so judging a matrix by its own strength misses the point.