Solving equation using diagonozation

[transgalactic]

i tried to solve it.
i got stuck near the end
http://img165.imageshack.us/img165/6914/img96931.th.gif

X is a variable of 2X2 type C

 

[HallsofIvy]

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

To summarize, you arrived at D= P^{-1}AP where D is the diagonal matrix
\begin{bmatrix}4 &amp; 0 \\ 0 &amp; -4\end{bmatrix}<br /> Since A^2= P^{-1}A^2P, we also have \sqrt{A}= P^{-1}\sqrt{D}P. Of course, <br /> \sqrt{D}= \begin{bmatrix}2 &amp;amp; 0 \\ 0 &amp;amp; 2i\end{bmatrix}

 

[transgalactic]

thanks :)