My problem: If I have two matrices $A$ and $B$ and $A$ is diagonalisable and $B$ isn't, can $AB$ be diagonalisable?
My solution: Those matrices are diagonisable if there is a regular matrix $Q$ that satisfies:
$AB=QD_AQ^{-1}QD_BQ^{-1}$
where $D_A, D_B$ are the digonal matrices with the eigenvalues of matrices $A$ and $B$ on their diagonal.
- I don't understand how $Q$ looks like, it's obviosly a matrix containing the eigenvectors, $A$'s eigenvectors?