Originally Posted by

**jayshizwiz** Let V and W be linear spaces onto field F.

T:V$\displaystyle \rightarrow$W is called Isomorphism from V over W iff it has these three properties:

1) T is a linear transformation

2) T is one-to-one

3) T is onto W

So by that definition of Isomorphism can I say that if KerT has more than one vector that transforms to $\displaystyle 0_w$ then those subspaces are not isomorphic.

Basically, I'm concluding that if two spaces are isomorphic to each other, only the zero vector of V transforms to the zero vector of W