Wikipedia claims: "a saddle point of a matrix is an element which is both the largest element in its column and the smallest element in its row".
Lots of programming puzzles also talk about finding the saddle point of a matrix. But I can't find any use for (or discussion of) a matrix saddle point except as a property of a payoff matrix for a two-player zero-sum game.
What I think has happened is that this definition was written in the context of two-player zero-sum payoff matrices (where it is useful) and that somebody picked up the idea as a programming exercise and now lots of texts talk about the "saddle point of a matrix" even though the definition is not useful outside of this context.
Am I missing something?
- Is this definition of a saddle point of a matrix useful in other contexts?
- Is there a nice connection between the concept of a saddle point of a matrix and the concept of a saddle point on the surface of a function (a critical point that is not a local minima or local maxima)?
Thanks!