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Diagonalizable matrix proof using minimal polynomial

  1. Sep 19, 2013 #1
    1. The problem statement, all variables and given/known data
    A matrix A[itex]\in[/itex]Mn(ℂ) is diagonalizable if and only if mA(x) has no repeated roots.


    2. Relevant equations
    If A[itex]\in[/itex]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)
     
  2. jcsd
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