I am asking to find unitary matrix $P$ such that $A=PDP^*$
given $A=\left(\begin{matrix} 1 & 3 & 3 \\ 3 & 1 & 3 \\ 3 & 3 & 1 \end{matrix}\right)$
I found that $P=\left(\begin{matrix} -1 & -1 & 1 \\ 1 & 0 & 1 \\ 0 & 1 & 1 \end{matrix}\right)$ and $D=\left(\begin{matrix} -2 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & 7 \end{matrix}\right)$
but I am not sure what to do now because the collums of $P$ is not orthogonal, so what I should do from here? should I apply $GS$ on those vectors in matrix $P$?