= Spectral Lipschitz bound from Frobenius distance
{title2=$|\langle L_A-L_B,f\rangle|\leq N^{-1/2}\|A-B\|_F$}
For equally sized <Hermitian matrices> and a real test <function> with <Lipschitz bound> one, the difference of its averages under their <empirical spectral measures> is at most $N^{-1/2}$ times the <Frobenius norm> of their difference. Pair the increasing <eigenvalues>, apply the <triangle inequality> and <Cauchy-Schwarz inequality>, then use the <Hoffman–Wielandt inequality>.
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