MHB Emeril's question at Yahoo Answers (invariant subspace).

[Fernando Revilla]

Here is the question:

What I have:

Since T: V --> V, R(T) = T(V)
For all x ∈ R(T), T(x) = ??

I'm not sure how to go from there.

Here is a link to the question:

Need help proving R(T), the image subspace is T-invariant.? - Yahoo! Answers

I have posted a link there to this topic so the OP can find my response.

 

[Fernando Revilla]

Hello Emeril,

Follow the steps
\begin{aligned}
x\in T(V)&\Rightarrow \exists u\in V:x=T(u)\\&\Rightarrow T(x)=T(T(u))\\&\Rightarrow T(x)\in T(V)\\&\Rightarrow T(V)\mbox{ is } T\mbox{-invariant}
\end{aligned}