I am checking for Sylvester's criterion. If one principal minor is negative does it mean the Hessian is negative semi-definite?
2026-03-25 23:13:08.1774480388
If one of the leading second order principal minor of a Hessian matrix is negative can I claim that the matrix is negative semi-definite?
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No, it does not mean that the matrix is negative semidefinite. In order to show that the matrix is negative semidefinite, you should show that all its principal minors are nonpositive.