It is known in multivariate calculus that, at a critical point $p_c = (x_{1c}, x_{2c}, ... , x_{nc})$ of the function $f(x_1, x_2, ... , x_n)$, if the Hessian is positive definite we have a local minimum and if it is negative definite we have a local maximum. However, I'm curious about the eigenvectors of the Hessian. Do they represent anything useful? For instance, do they represent an ellipsoid inside of which $f(p_c)$ is the global maximum/minimum?
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Yes, it is. Sorry about that. That question answers it handily. – Michael Stachowsky Apr 12 '17 at 17:34
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@amd: please see the above comment thread – Michael Stachowsky Apr 12 '17 at 17:49