- #1
NATURE.M
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Homework Statement
So my text states the proposition:
If V and W are finite dimensional vector spaces, then there is an isomorphism T:V→W ⇔ dim(V)=dim(W).
So, in an example the text give the transformation T:P[itex]_{3}[/itex](R)→P[itex]_{3}[/itex](R)
defined by T(p(x)) = x dp(x)/dx.
Now I understand T is not an isomorphism since ker(T) = span(1) , the set of all constant polynomial functions. But by the above theorem since the dim(V) = dim(W), T would an isomorphism.
So I'm a bit confused.