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How to calculate matrixA^100 manually

  1. Jan 4, 2010 #1
    hi guys...my teacher wants me to calculate A^100 of a 3*3 matrix by hand...i cant use matlab for this...how do i do it....i cant imagine multiplying 100 time....
    help me
     
  2. jcsd
  3. Jan 4, 2010 #2

    Borek

    User Avatar

    Staff: Mentor

    (A^50)^2

    But most likely this is a specific matrix, with interesting properties that make it easy to calculate power no matter how high.
     
  4. Jan 4, 2010 #3
    Check if the matrix is diagonalizable or, if it isn't, use the Jordan form to write it as a sum of a diagonal plus nilpotent matrix.
     
  5. Jan 5, 2010 #4
    thanks guys...will try all
     
  6. Jan 7, 2010 #5
    Yet another way is to use the minimal polynomial to express A^100 in terms of I, A, A^2.
     
  7. Jan 7, 2010 #6
    i actually did it by finding the eigen values of the matrix....
    anyways thank u guys for responding
     
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