Does $\mbox{tr}(A^2) \geq 0$ hold for any real matrix $A$?
I think this is true but I am unable to prove this. Any further help is appreciated.
2026-03-25 09:23:56.1774430636
Is $\mbox{tr}(A^2)$ always nonnegative?
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Let $A=\left[\begin{matrix}0 & -1\\2 & 0\end{matrix}\right]$. Square it and see what happens...