# Solving equation using diagonozation

1. Mar 3, 2009

### transgalactic

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

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

3. Mar 3, 2009

thanks :)