# Clearly explain Isomorphisms

1. Mar 27, 2005

### TimNguyen

Could someone clearly explain this subject? Going over some linear algebra the moment and I don't see what this topic matter is really about (isomorphisms).

2. Mar 27, 2005

### matt grime

Isomophisms are always (in any sense) about bijective maps that preserve the structure of the objects. Bijective means invertible. So if X and Y are isomorphic (ie there are isomorphisms between them) then we are saying X and Y are equivalent (but not necessarily equal) objects in what ever sense we are talking about.

Here an isomorphism is a linear map that has an inverse (that is also a linear map).