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eigenvalues of matrices or operators

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Bounds on Eigenvalues After Skew-Symmetric Perturbation

I am trying to upper bound the eigenvalues of their sum: $$\mathbf{A} = \mathbf{J} + \mathbf{L}$$ in terms of the eigenvalues of $\mathbf{J}$. … It is easy enough to show that the eigenvalues of the symmetric part of $\mathbf{A}$ are equal to the eigenvalues of the symmetric part of $\mathbf{J}$, but can something be said about the eigenvalues