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Homework Help: Diagonal matrix

  1. Oct 11, 2008 #1
    1. The problem statement, all variables and given/known data

    Suppose the matrix A , B are diagonalizable and have the same eigenvectors. Show AB=BA

    2. Relevant equations

    3. The attempt at a solution

    There exists a matrix P s.t. (P^-1)AP=(P^-1)BP

    I played around with this, and could not get anywhere..
  2. jcsd
  3. Oct 11, 2008 #2


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    If A is diagonalizable then there is a basis where it's a diagonal matrix. Then all of the basis vectors are eigenvectors. If B has the same eigenvectors then it's also a diagonal matrix in the same basis. Now you just have to show two diagonal matrices commute.
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