For functions on $\mathbb{R}^2$, it lets you classify extreme points. When function is log-likelihood, it gives volume of the region where maximum likelihood estimates tend to fall. Are there other places it comes up?
Determinant of the Hessian, what is it good for?
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calculus
matrices
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0Browsing the Wikipedia article leads you to http://en.wikipedia.org/wiki/Blob_detection#The_determinant_of_the_Hessian . – 2010-09-15
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0I believe the determinant of the Hessian of f(x,y) gives you the Gaussian curvature of the graph of f. – 2010-09-15