Abstract: This paper discusses canonical forms of vector ARMA representations for a linear, time-invariant system. Both the Kronecker index and the scalar-component model (SCM) approaches are presented and discussed. The Kronecker index approach results in an Echelon form. For the SCM approach, a canonical SCM representation is introduced. The relation between Kronecker indices and orders of scalar component models is also established.
Key words and phrases: Echelon form, Hankel matrix, Kronecker index, scalar component models, vector ARMA models.