Suppose that we have a positive definite matrix $X$ and its entry-wise positive version $Y=|X|$ where $\forall i, j \;\; y_{ij}=|x_{ij}|$. Is there any relationship between their eigen-decompositions, more specifically their eigenvectors? If not, are there stronger constraints on $X$ that result in a relationship?
2026-04-07 04:43:00.1775536980
Relation between the eigendecomposition a PD matrix and its entry-wise positive counterpart
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