  We introduce matrix and its block to the Dung's theory of argumentation
frameworks. It is showed that each argumentation framework has a matrix
representation, and the common extension-based semantics of argumentation
framework can be characterized by blocks of matrix and their relations. In
contrast with traditional method of directed graph, the matrix way has the
advantage of computability. Therefore, it has an extensive perspective to bring
the theory of matrix into the research of argumentation frameworks and related
areas.
