Editing Smith normal form (section)

== Applications ==

The Smith normal form is useful for computing the [[homology (mathematics)|homology]] of a [[chain complex]] when the chain modules of the chain complex are [[Finitely generated module|finitely generated]].  For instance, in [[topology]], it can be used to compute the homology of a finite [[simplicial complex]] or [[CW complex]] over the integers, because the boundary maps in such a complex are just integer matrices.  It can also be used to determine the [[invariant factor]]s that occur in the [[structure theorem for finitely generated modules over a principal ideal domain]], which includes the [[fundamental theorem of finitely generated abelian groups]].

The Smith normal form is also used in [[control theory]] to compute [[transmission and blocking zeros]] of a [[transfer function matrix]].<ref>{{Cite book|title=Multivariable feedback design|last=Maciejowski|first=Jan M.|date=1989|publisher=Addison-Wesley|isbn=0201182432|location=Wokingham, England|oclc=19456124}}</ref>