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Diagonalizable and Nilpotent

  1. Dec 15, 2008 #1
    1. write the given matrix A as the sum of a diagonalizable matrix and a nilpotent matrix.

    A =

    7, 3, 3, 2
    0, 1, 2,-4
    -8,-4,-5,0
    2, 1, 1, 3

    2. Relevant equations

    3. The eigenvalues are 1, -1, 3 and the associated eigenvalues are

    (1,-2,0,0)
    (0,1,-1,0)
    (1,-2,0,1), respectively.

    Some steps in solving this question/ types of these questions would be amazing. Please explain in layman's terms, because I'm a little over my head :)
     
  2. jcsd
  3. Dec 16, 2008 #2
    Using your notation,

    B=

    (0,3,3,2)
    (0,0,2,-4)
    (0,0,0,0)
    (0,0,0,0)

    Then B is nilpotent. Likewise for the bottom half. But do they commute?
     
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