= Two-by-two anticommutator characteristic polynomial
{title2=$\chi_{B\mapsto AB+BA}(t)=(t-\operatorname{tr}A)^2(t^2-2t\operatorname{tr}A+4\det A)$}
If $A$ is diagonalizable, the <anticommutator> map $B\mapsto AB+BA$ has <eigenvalues> $2\lambda_1$, $\lambda_1+\lambda_2$ twice, and $2\lambda_2$. Their product gives the displayed <characteristic polynomial>. The <density of diagonalizable complex matrices> and continuity of polynomial coefficients prove the formula also for defective matrices.
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