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More specifically, suppose I have a known matrix $X\in\mathbb{R}^{d\times n}$ and an unkown vector $\alpha \in \mathbb{R}^n$.

What can be said about the eigenvectors of $\alpha\alpha^T \odot X^T X$ in terms of the eigenvectors of $X^T X$?

(The notation $\odot$ means $[A\odot B]_{ij}=A_{ij}B_{ij}$).

notarobot
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    You may find this interesting: http://math.stackexchange.com/questions/711918/eigenvalues-and-eigenvectors-of-hadamard-product-of-two-positive-definite-matric – JessicaK Dec 13 '14 at 06:00
  • That is interesting. Too bad there is no answer :) – notarobot Dec 13 '14 at 06:03

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