1. ## Isomorphism

Let V and W be linear spaces onto field F.

T:V $\rightarrow$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 $0_w$ 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

2. Originally Posted by jayshizwiz
Let V and W be linear spaces onto field F.

T:V $\rightarrow$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 $0_w$ 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
u are right since if the kernel have more than two vectors say u,v $u\ne v \;$ then
T(u) = T(v) = 0 not one-one