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

Homework Help: Matrix question

  1. Nov 29, 2006 #1
    I have a 3x3 symmetrical matrix A:

    1, 8^.5, 0
    8^.5, 1, 8^.5
    0, 8^.5, 1

    that I need to find A^5 for. Is there a method aside from brute force multiplication to do so?
  2. jcsd
  3. Nov 29, 2006 #2


    User Avatar
    Homework Helper

    A fact which should be useful is that the product of symmetric matrices is symmetric itself.
  4. Nov 30, 2006 #3
    Ok, how does that help?
  5. Nov 30, 2006 #4


    User Avatar
    Homework Helper

    It reduces the number of multiplications you have to do. But it's still a semi-brute multiplication method. Hope someone passes by with a better suggestion perhaps. :tongue2:
  6. Nov 30, 2006 #5


    User Avatar
    Science Advisor

    Since that is a symmetric matrix, it can be "diagonalized". That is there exist an invertible matrix C and a diagonal matrix D such that D= CAC-1. Then A= C-1DC. Then A5= C-1D5C. D is the matrix having the eigenvalues of A (which are easy to find) on its main diagonal, 0s off the diagonal. C is a matrix having the corresponding eigenvectors of A as columns.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook