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## Homework Statement

Prove: if (Q^-1)AQ=D, then each column of Q is an eigenvector of A.

## Homework Equations

A vector v is an eigenvector of A iff there exists a scalar λ such that:

Av=λv

## 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.

Thanks!