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mock 2014 positive definite even though negative

Hello,

For the 2rd question on poisson regression: I don't understand why the negative of a positive definite matrix would still be positive definite?

Thanks in advance for the help

m14q2.JPG

The Hessian is derived for the log-likelihood log p(y|X,β) (parts (a)-(c)). Whereas part (d) asks for the convexity of the "negative" of the log-likelihood, so one would be looking at -H instead of H, I believe. It would be nice if someone else could confirm this?

I'm not a TA but I confirm :)

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