Prove: if (Q^-1)AQ=D, then each column of Q is an eigenvector of A.
A vector v is an eigenvector of A iff there exists a scalar λ such that:
The Attempt at a Solution
Suppose (Q^-1)AQ=D. We need to show each column of Q is an eigenvector of A.
At this point, should I actually write out (Q^-1)AQ=D in general element form? That is, should I write out (Q^-1),A,Q,D in the form of nxn matrices?
I'm honestly not even sure how to begin the proof, but any help would be appreciated.