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
[tex]\begin{bmatrix}4 & 0 \\ 0 & -4\end{bmatrix}<br /> Since $A^2= P^{-1}A^2P$, we also have $\sqrt{A}= P^{-1}\sqrt{D}P$. Of course, <br /> $$\sqrt{D}= \begin{bmatrix}2 & 0 \\ 0 & 2i\end{bmatrix}$$[/tex]

 

[transgalactic]

thanks :)