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Exercise 5.3.6

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For two symmetric matrices $S$ and $T$ , we have $λ_{\max} (S + T) \leq λ_{\max} (S) + λ_{\max} (T)$ according to the equation (15) on page 172 from “III.2 Interlacing Eigenvalues and Low Rank Signals”.

So we have $λ_{\max} (Ȳ) = λ_{\max} (p_{1} Y_{1} + \dots + p_{n} Y_{n}) \leq λ_{\max} (p_{1} Y_{1}) + \dots λ_{\max} (p_{n} Y_{n}) = p_{1} λ_{\max} (Y_{1}) + \dots + p_{n} λ_{\max} (Y_{n}) = E [λ_{\max} (Y)]$

niuers

2020-03-20 00:00

Exercise 5.3.6

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