Understanding Isomorphisms in Linear Transformations?

[Dgray101]

Hey I have a problem in which I need to show that a linear transformation is an isomorphism with another linear transformation. However I don't really understand what an isomorphism is, and how you would even determine it??

I already showed that the Kernal of one transformation was the same as the Range of another transformation is that helps any? I am looking for help on the concept and idea, I wouldn't consider this to be a homework problem? I'm new here, don't really know the rules and regulations that well.

 

[Axiomer]

Two vector spaces V and W are said to be isomorphic if there is a bijective (invertible) linear transformation T:V->W, in which case T is called an isomorphism from V to W. It doesn't make sense to speak of a linear transformation being an isomorphism with another linear transformation, they would just be isomorphisms on their own. Posting the question would help clear things up more.