Smith Form

• a square polynomial matrix *Q(s)* is *unimodular* iff det *Q(s)* is constant.

• Let *Q(s)* be a (*p*×*m*) polynomial matrix. Then the *normal* *rank* of *Q(s),* denoted *normalrank* *(Q(s))*, is the maximally
possible rank of *Q(s)* for at least one *s*Î **C**.

Example:

•* Smith
form*: Let
*P(s)* be any polynomial matrix,
then there exist unimodular matrices *U(s),* *V(s) *Î **R**[s] such that

where gi(*s*) divides gi+1(*s*) and *r* is the normal rank of *P(s).*