The matrix, as an extended pattern representation to the vector, has proven to be effective in feature extraction. But the subsequent classifier following the matrix-pattern-oriented feature extraction is generally still based on the vector pattern representation (namely MatFE+VecCD), where it has been demonstrated that the effectiveness in classification just attributes to the matrix representation in feature extraction. This paper looks at the possibility of applying the matrix pattern representation to both feature extraction and classifier design. To this end, we propose a so-called fully matrixized approach, i.e. the matrix-pattern-oriented feature extraction followed by the matrix-pattern-oriented classifier design (MatFE+MatCD). To more comprehensively validate MatFE+MatCD, we further consider all the possible combinations of feature extraction (FE) and classifier design (CD) on the basis of patterns represented by matrix and vector respectively, i.e. MatFE+MatCD, MatFE+VecCD, ...