Coprime
Factorization over RH¥

•Two polynomials *m(s)* and *n(s)* are coprime if the only common factors are
constants.

•Two transfer functions *m(s)* and *n(s)* in *RH**¥* are coprime if the only common factors are stable
and invertible transfer functions (units): I.e. *h, mh**-1**, nh**-1* Î *RH**¥* _ *h**-1* Î *RH**¥*

Equivalent, there exists *x,y* Î *RH**¥** * such
that

•Matrices *M* and *N* in *RH**¥* are right coprime if there exist matrices *X**r* and *Y**r* in *RH**¥* such that

•Matrices
and in *RH**¥* are left coprime if there exist matrices *X**l* and *Y**l* in *RH**¥* such that