# Prove zero vector

• Feb 2nd 2010, 05:14 PM
wopashui
Prove zero vector
Let $\lambda$ and $\mu$ be distinct eigenvalues for $T:R^n-->R^n$and let the corresponding eigenspaces be $V_\lambda$ and $V_\mu$ respectively. Prove that the only vector common to both $V_\lambda$ and $V_\mu$ is the zero vector.
• Feb 2nd 2010, 05:30 PM
Bruno J.
What do you get if you apply T to a vector lying in the intersection?
• Feb 3rd 2010, 09:32 AM
Runty
Look at this topic:

http://www.mathhelpforum.com/math-he...ro-vector.html