Proof about eigenvalues/vectors of a linear transformation
I had to say whether the following affirmation was true or not and explain. I fell in love with the proof I gave : (I hope there's no flaws in it)
Let be a linear transformation and let and be 2 eigenvectors of with eigenvalues and respectively. If is linear independent.
I say true : Proof :
I have to prove , so I'll prove which is equivalent. In other words I have to prove that linear dependent implies .
So we have linear dependent such that .
We have that .
Is there any flaw?