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The celebrated Hoffman--Wielandt theorem states that there exists a permutation $\\pi$ of $\\{1,\\ldots,n\\}$ such that $\\left(\\sum_{i=1}^{n}\\big|\\widetilde{\\lambda}_{\\pi(i)}-\\lambda_{i}\\big|^{2}\\right)^{1\\over 2}$ is no larger than the Frobenius norm of $\\widetilde{A}-A$. However, if either $A$ or $\\widetilde{A}$ is non-normal, this result does not hold in general. 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The celebrated Hoffman--Wielandt theorem states that there exists a permutation $\\pi$ of $\\{1,\\ldots,n\\}$ such that $\\left(\\sum_{i=1}^{n}\\big|\\widetilde{\\lambda}_{\\pi(i)}-\\lambda_{i}\\big|^{2}\\right)^{1\\over 2}$ is no larger than the Frobenius norm of $\\widetilde{A}-A$. However, if either $A$ or $\\widetilde{A}$ is non-normal, this result does not hold in general. 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