1. The problem statement, all variables and given/known data If the matrix of a linear transformation relative to a basis is non-diagonalisable, then for any other choice of basis, it too will be non-diagonalisable. Prove this is the case. 2. Relevant equations Similar matrices. 3. The attempt at a solution Let APB=[T]BPB, where A is a nxn matrix. But I'm stuck. Not sure what to do next.