A matrix representation of a linear map depends on choice of basis. Change-of-basis matrix P transforms coordinates: [v]_{B'} = P^{-1}[v]_B; matrix A becomes P^{-1}AP.
A matrix representation of a linear map depends on choice of basis. Change-of-basis matrix P transforms coordinates: [v]_{B'} = P^{-1}[v]_B; matrix A becomes P^{-1}AP.