Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar

    Staff: Mentor


    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook