= Hoffman–Wielandt inequality
{c}
{title2=$\min_\pi\sum_i|\lambda_i(A)-\lambda_{\pi(i)}(B)|^2\leq\|A-B\|_F^2$}
For two <normal matrices> of the same size, a pairing of their <eigenvalues> has squared Euclidean discrepancy at most the squared <Frobenius norm> of their difference. For <Hermitian matrices>, the increasing real <eigenvalue> order gives such a pairing, because it minimizes squared discrepancy. For real <symmetric matrices>, the norm square is $\operatorname{Tr}(A-B)^2$.
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