ABSTRACT
Let V be an n-dimensional vector space over a field F . Given any linear operator T : V → V and any ordered basis X of V , recall from Chapter 6 that there is a matrix A = [T ]X in Mn(F ) that represents T relative to the basis X. If we switch from X to another ordered basis Y , the matrix A is replaced by a similar matrix of the form [T ]Y = P
−1AP , where P ∈ Mn(F ) is some invertible matrix (specifically, P is the matrix of idV relative to the input basis Y and output basis X).
