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Square Root of a 2x2 Matrix (by diagonalization)

  1. Oct 9, 2011 #1
    1. The problem statement, all variables and given/known data
    Show that the


    -1 -2
    4 -1


    2x2 matrix has one square root.

    2. Relevant equations

    det(A-λI) to find Eigenvalues
    (A-λI)v=0 to find Eigenvectors
    A1/2 = V D1/2 V-1 to find the square root of A where V is the created matrix with the eigenvectors of A, and D is the diagonalized matrix A

    3. The attempt at a solution

    I know I can use diagonalization to find the square root:
    Using the formula its eigenvalues are -1+(-32)1/2 and -1-(-32)1/2
    But I don't know how to find the eigenvectors given that (-32)1/2 it's a complex number.
     
    Last edited: Oct 9, 2011
  2. jcsd
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