# Saddle Point

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## saddle point

[′sad·əl ‚pȯint] (geology)

(mathematics)

A point where all the first partial derivatives of a function vanish but which is not a local maximum or minimum.

For a matrix of real numbers, an element that is both the smallest element of its row and the largest element of its column, or vice versa.

For a two-person, zero-sum game, an element of the payoff matrix that is the smallest element of its row and the largest element of its column, so that the corresponding strategies are optimal for each player, given the strategy chosen by the other player.

McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

The following article is from

*The Great Soviet Encyclopedia*(1979). It might be outdated or ideologically biased.## Saddle Point

a critical point of a first-order differential equation. In a neighborhood of a saddle point, four half-line integral

curves enter the critical point. Between the four curves there are four regions, each of which contains a family of integral curves resembling hyperbolas (see Figure l). The pattern of integral curves in a neighborhood of a saddle point is reminiscent of the contour lines of a hyperbolic paraboloid, which has the shape of a saddle—hence the name of the critical point.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.