A matrix project structure occurs in organizations where there are groups representing both functions (e.g. accounting, IT, manufacturing) and products. The project manager needs to draw from and manage people from both dimensions of the matrix to have a successful project team.
There are three variations of matrix projects/organizations:
Weak matrix: the functional managers maintain authority over their employees and the PM has limited authority
Balanced matrix: the functional managers and project managers share authority and power; this is ideal however the balance is often difficult to maintain when there are strong personalities involved
Strong matrix: the project manager is responsible for the project and the functional manager assigns resources as necessary