# Homework Help: Diagonalizable matrix proof using minimal polynomial

1. Sep 19, 2013

### rideabike

1. The problem statement, all variables and given/known data
A matrix A$\in$Mn(ℂ) is diagonalizable if and only if mA(x) has no repeated roots.

2. Relevant equations
If A$\in$Hom(V,V) = {A:V→V | A is a linear map}, the minimal polynomial of A, mA(x), is the smallest degree monic polynomial f(x) such that f(A)=0.

3. The attempt at a solution
In one direction, want to prove if mA(x) has repeated roots, then there are not n linearly independent eigenvectors in A (with A n X n)