Plot of y = x ^{3} with a saddlepoint at (0,0). In mathematics, a saddle point is a point of a function (of one or more variables) which is both a stationary point and a point of inflection. Since it is a point of inflection, it is not a local extremum. Image File history File links I created this graph using software I wrote and grant full license to anyone to use, copy, and distribute. ...
Image File history File links I created this graph using software I wrote and grant full license to anyone to use, copy, and distribute. ...
Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations by or about: Mathematics Look up Mathematics in Wiktionary, the free dictionary Wikimedia Commons has more media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ...
The word point can refer to: a location in physical space a unit of angular measurement; see navigation point is a typographic unit of measure in typography equal inch or sometimes approximated as inch; on computer displays it should be equal to point in typography if the correct display resolution...
In general, a function is part of an answer to a question about why some object or process occurred in a system that evolved or was designed with some goal. ...
In computer science and mathematics, a variable is a symbol denoting a quantity or symbolic representation. ...
In mathematics, particularly in calculus, a stationary point is a point on the graph of a function where the tangent to the graph is parallel to the xaxis or, equivalently, where the derivative of the function equals zero (known as a critical number). ...
In mathematics, particularly in calculus, a stationary point is a point on the graph of a function where the tangent to the graph is parallel to the xaxis or, equivalently, where the derivative of the function equals zero (known as a critical number). ...
A graph illustrating local min/max and global min/max points In mathematics, a point x* is a local maximum of a function f if there exists some ε > 0 such that f(x*) ≥ f(x) for all x with xx* < ε. ...
For a function of a single variable, such a point is one where the first derivative is zero, and the second derivative changes sign. For example, the function y = x^{3} has such a point at the origin. The derivative in mathematics (specifically, differential calculus) is a quantity that measures, on continuous functions, the limit of a rate of change, , as approaches 0. ...
In mathematics, the origin of a coordinate system is the point where the axes of the system intersect. ...
Saddle point in the graph of z=x²y² For a function of two or more variables, the surface at a saddlepoint resembles a saddle that curves up in one ore more directions, and curves down in one or more other directions (like a mountain pass). In terms of contour lines, a saddle point can be recognised, in general, by a contour that appears to intersect itself. For example, two hills separated by a high pass will show up a saddle point, at the top of the pass, like a figureeight contour line. Wikipedia does not have an article with this exact name. ...
Wikipedia does not have an article with this exact name. ...
In mathematics, a surface is a twodimensional manifold. ...
Tack is any of the various accessories worn by horses in the course of their use as domesticated animals. ...
In a range of hills, or especially of mountains, a pass (also gap, notch, col, saddle, bwlch or bealach) is a lower point that allows easier access through the range. ...
Contour map A contour line (also level set, isogram or isarithm) for a function of two variables is a curve connecting points where the function has a particular value. ...
In mathematics, a lemniscate is a type of curve described by a Cartesian equation of the form: Graphing this equation produces a curve similar to . ...
More formally, given a real function F(x,y) of two real variables, the Hessian matrix H of F is a 2×2 matrix. If it is indefinite (neither H nor −H is positive definite) then in general it can be reduced to the Hessian of the function In mathematics, the Hessian matrix is the square matrix of second partial derivatives of a scalarvalued function. ...
In mathematics, a definite bilinear form B is one for which B(v,v) has a fixed sign (positive or negative) when it is not 0. ...
 x^{2} − y^{2},
at the point (0,0). This function has a saddle point there, curving up along the line y = 0 and down along the line x = 0. In fact if H is a nonsingular matrix (general case) and F is smooth enough, this is the correct local model for a stationary point of F that is not a local maximum nor a local minimum. If H has rank < 2 one cannot be certain in the same way about the local behaviour. In mathematics and especially linear algebra, an nbyn matrix A is called invertible, nonsingular or regular if there exists another nbyn matrix B such that AB = BA = In, where In denotes the nbyn identity matrix and the multiplication used is ordinary matrix multiplication. ...
A graph illustrating local min/max and global min/max points In mathematics, a point x* is a local maximum of a function f if there exists some ε > 0 such that f(x*) ≥ f(x) for all x with xx* < ε. ...
A graph illustrating local min/max and global min/max points In mathematics, a point x* is a local maximum of a function f if there exists some ε > 0 such that f(x*) ≥ f(x) for all x with xx* < ε. ...
In physics, wet electrons are a saddle point between electrons in liquid and electrons in solid. This article needs to be cleaned up to conform to a higher standard of article quality. ...
See also
