I have a multivariate function in one of whose critical points the Hessian matrix is singular. Is there any general method to determine the type of this critical point? Would be worth plotting the function in the direction of the eigenvector associated to a zero eigenvalue of the Hessian matrix?

  • The Hessian gives you a quadric approximation to the function in a neighborhood of the critical point. Examining the principal axes of this quadric should give you an idea of the function’s behavior near that point. – amd Sep 14 at 19:24

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