If the hessian evaluated at a critical point is positive (negative) definite, then we can conclude that it's a local minimum (maximum) there. If the hessian is indefinite (both negative and positive eigenvalues), then it's a saddle point. What happens if the Hessian is positive SEMI-definite?

Gorlandint

Gorlandint

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2022-08-16

If the hessian evaluated at a critical point is positive (negative) definite, then we can conclude that it's a local minimum (maximum) there. If the hessian is indefinite (both negative and positive eigenvalues), then it's a saddle point.
What happens if the Hessian is positive SEMI-definite?

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Kelsie Marks

Kelsie Marks

Beginner2022-08-17Added 17 answers

If the hessian evaluated at a critical point is positive (negative) definite, then we can conclude that it's a local minimum (maximum) there. If the hessian is indefinite (both negative and positive eigenvalues), then it's a saddle point.
What happens if the Hessian is positive SEMI-definite?

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