help with hessian matrix

Hi there.

If i have a 4x4 hessian matrix, how can i determine if its a local max/min or saddle, aside from using the eigenvalue method? I was wondering if there was another way of doing it that wouldn't require a calculator after that many steps.

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Originally Posted by Kuma

If i have a 4x4 hessian matrix, how can i determine if its a local max/min or saddle, aside from using the eigenvalue method?

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Sylvester's criterion.

Cant believe this slipped my mind but how about just finding determinants of the submatricies to find out the nature of the point? easier than doing the eigenvalue method.