Editing Saddle point (section)

==Examples==
In a two-player [[zero-sum (game theory)|zero sum]] game defined on a continuous space, the [[Nash equilibrium|equilibrium]] point is a saddle point.

For a second-order linear autonomous system, a [[critical point (mathematics)|critical point]] is a saddle point if the [[Characteristic equation (calculus)|characteristic equation]] has one positive and one negative real [[Eigenvalues and eigenvectors|eigenvalue]].<ref>{{harvnb|von Petersdorff|2006}}</ref>

In optimization subject to equality constraints, the first-order conditions describe a saddle point of the [[Lagrange multiplier|Lagrangian]].