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Solving equation using diagonozation

  1. Mar 3, 2009 #1
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Mar 3, 2009 #2


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    It's pretty clear that equation has no solution over the real numbers.

    To summarize, you arrived at [itex]D= P^{-1}AP[/itex] where D is the diagonal matrix
    [tex]\begin{bmatrix}4 & 0 \\ 0 & -4\end{bmatrix}
    Since [itex]A^2= P^{-1}A^2P[/itex], we also have [itex]\sqrt{A}= P^{-1}\sqrt{D}P[/itex]. Of course,
    [tex]\sqrt{D}= \begin{bmatrix}2 & 0 \\ 0 & 2i\end{bmatrix}[/tex]
  4. Mar 3, 2009 #3
    thanks :)
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