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This question is about the two vectors $w'$ and $y$ that are necessary for the argument in section $7$ (page 6) of this paper by Terence Tao and Van Vu, https://arxiv.org/abs/math/0703307 (that ...

Let $A\in\mathbb{R}^{n\times n}$ be diagonalisable (over $\mathbb{C}$) with pairwise distinct eigenvalues $\lambda_1,\ldots,\lambda_n\in\mathbb{C}$, and suppose that $$\tag{1}S^{-1}\cdot A\cdot S = \...