For rotationally invariant random matrices, entrywise nonlinearities are asymptotically equivalent to a linear combination of the original matrix and an independent Gaussian matrix, with coefficients computed from the function and the matrix variance.
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Entrywise application of non-linear functions on orthogonally invariant matrices
For rotationally invariant random matrices, entrywise nonlinearities are asymptotically equivalent to a linear combination of the original matrix and an independent Gaussian matrix, with coefficients computed from the function and the matrix variance.