
Prove zero vector
Let $\displaystyle \lambda$ and $\displaystyle \mu$ be distinct eigenvalues for $\displaystyle T:R^n>R^n $and let the corresponding eigenspaces be $\displaystyle V_\lambda$ and $\displaystyle V_\mu$ respectively. Prove that the only vector common to both $\displaystyle V_\lambda$ and $\displaystyle V_\mu$ is the zero vector.

What do you get if you apply T to a vector lying in the intersection?

Look at this topic:
http://www.mathhelpforum.com/mathhe...rovector.html
I already asked the question earlier and had it answered.