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Deep learning Book by Goodfellow

In the second paragraph it is mentioned that eigenvector of $H$ is rescaled by a factor of $\frac{\lambda_i} {\lambda_i +\alpha}$ What exactly meant by that ?

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    $\begingroup$ Can you work out the answer if you write down the inverse of $$ \begin{bmatrix} \lambda_1 & 0 \\ 0 & \lambda_2 \end{bmatrix} + \alpha I? $$ $\endgroup$ – Sycorax says Reinstate Monica Feb 9 '19 at 19:36
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    $\begingroup$ This is explained at the end of my post at stats.stackexchange.com/a/220324/919. $\endgroup$ – whuber Feb 9 '19 at 19:54
  • $\begingroup$ Thanks @Sycorax for your great answers. This solved my ambiguity. :) $\endgroup$ – OmegaD Feb 9 '19 at 20:07