This paper studies the matrix algebra properties of the collective behavior of liner multi-agent dynamic systems in
directed network, where the agent is with dynamical order one or two. By means of matrix analysis approach, the coefficient
matrix of system can be transformed into Frobenius canonical form. Thus, the system is decomposed into several basic
independent subsystems and basic non-independent subsystems. Based on the study of diagonally dominant matrices with
the sum of entries in each row being zero, some properties of coefficient matrix are obtained, which play a key role in the
collective behavior of liner multi-agent dynamic systems. Thus, the study of collective behavior of system is reduced to some
elementary linear algebra problems.