  We introduce matrix and its block to the Dung's theory of argumentation
framework. It is showed that each argumentation framework has a matrix
representation, and the indirect attack relation and indirect defence relation
can be characterized by computing the matrix. This provide a powerful
mathematics way to determine the "controversial arguments" in an argumentation
framework. Also, we introduce several kinds of blocks based on the matrix, and
various prudent semantics of argumentation frameworks can all be determined by
computing and comparing the matrices and their blocks which we have defined. In
contrast with traditional method of directed graph, the matrix method has an
excellent advantage: computability(even can be realized on computer easily).
So, there is an intensive perspective to import the theory of matrix to the
research of argumentation frameworks and its related areas.
