Definition. A matrix organizational structure is a company structure in which the reporting relationships are set up as a grid, or matrix, rather than in the traditional hierarchy. In other words, employees have dual reporting relationships-generally to both a functional manager and a product manager.or Teachers for Schools for Companies. A matrix organizational structure is one of the most complicated reporting structures a company can implement. Read on to learn why a company might implement a matrix structure, and the advantages and disadvantages for both company and staff.