A Matrix structure is basically an organizational structure which consists of teams of people which are created by bringing together people from various areas of the business. These teams are created for a specific task or project and are led by a project manager. When the task of the team is accomplished the group is disbanded.
On the other hand, a hierarchical structure is a commonly used in large organizations. It is characterized by a single person or a group of power at the top who have a number of people underneath. These few people are in turn responsible for managing hundreds of employees under them.
These two structures are completely different in nature. Matrix structure is more open and participative whereas a hierarchical structure is closed and bureaucratic in nature.