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Finding the square root of a matrix!

  1. Nov 28, 2011 #1
    1. The problem statement, all variables and given/known data

    Let A be the matrix:
    -5 -3
    18 10

    Find an invertible matrix X so that XAX-1 is diagonal. Use this to find a square root of the matrix A.

    2. Relevant equations

    DetA - xI
    (A-[itex]\lambda[/itex]I)v = 0

    3. The attempt at a solution

    So, I found DetA- xI, which gave me the eigenvalues 4 and 1. I found the eigenvectors for each value, giving me X =
    -1 -1
    3 2

    Now what confuses me is finding the square root of A. I understand that XD1/2X-1 will give me that, so would I just multiply X by D1/2 , and then by X-1? I tried that, and it gave me A=

    -1 -1
    6 4
     
  2. jcsd
  3. Nov 28, 2011 #2

    I like Serena

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    If you multiply your final matrix by itself, what do you get?
     
  4. Nov 28, 2011 #3
    The original matrix A! Thank you! I don't know how I didn't think of that to check my work..
     
  5. Nov 28, 2011 #4

    I like Serena

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