Complexity of Finding the Eigendecomposition of a *Symmetric* Matrix This is a specialized version of a previous question:
    Complexity of Finding the Eigendecomposition of a Matrix .

For NxN symmetric matrices, it is known that O(N^3) time suffices to compute the eigen decomposition.  The question is: can we achieve sub-cubic complexity?  Thanks.
I know this is a really old question, but it seems like this recent paper https://arxiv.org/abs/1912.08805 improves the runtime to $O(n^\omega)$, down from $O(n^3)$.