Let's say that I have a matrix where each entry has it's own standard error. $\textbf{A} \pm \textbf{$\delta$ A}$. What would be the error of $Tr(\textbf{A}^2)$?
Is the error of $\textbf{A}^2$ just $\delta \textbf{A}^2 = \textbf{A}\textbf{$\delta$ A}+\textbf{$\delta$ A} \textbf{A}+ \delta \textbf{A} \delta\textbf{A}$ ?