• Suppose
has full row normal rank. Then *z**0* is an invariant zero iff there exist *0**¹** **y*Î **C**n and *v*Î **C**p such that

Moreover, if *v* = 0, then *z**0* is also a non-observable mode.

• G(s) has
full column(row) normal rank if and only if has full column (row) normal
rank.

This follows by noting that

and

• Let be a minimal
realization. Then *z**0* is a transmission of *G(s)* iff it is an invariant
zero of the minimal realization.