Module isomorphism
= Module isomorphism
A <module isomorphism> is a bijection of <modules> over the same <ring> preserving addition and scalar multiplication. Its inverse preserves these operations too. When a <linear operator> $T$ gives a <vector space> an $F[t]$-<module> structure by $t\cdot v=T(v)$, a <module isomorphism> is exactly an invertible <linear map> intertwining the two operators. This translates classification of <modules> into <matrix similarity> and <rational canonical form>.