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A field K is said to be an extension field (or field extension, or extension), denoted K/F, of a field F if F is a subfield of K. For example, the complex numbers are an ...

A geodesic is a locally length-minimizing curve. Equivalently, it is a path that a particle which is not accelerating would follow. In the plane, the geodesics are straight ...

An algorithm which can be used to find integer relations between real numbers x_1, ..., x_n such that a_1x_1+a_2x_2+...+a_nx_n=0, with not all a_i=0. Although the algorithm ...

Stationary iterative methods are methods for solving a linear system of equations Ax=b, where A is a given matrix and b is a given vector. Stationary iterative methods can be ...

The scalar form of Laplace's equation is the partial differential equation del ^2psi=0, (1) where del ^2 is the Laplacian. Note that the operator del ^2 is commonly written ...

Linear programming, sometimes known as linear optimization, is the problem of maximizing or minimizing a linear function over a convex polyhedron specified by linear and ...

The absolute value of a real number x is denoted |x| and defined as the "unsigned" portion of x, |x| = xsgn(x) (1) = {-x for x<=0; x for x>=0, (2) where sgn(x) is the sign ...

A 24-dimensional Euclidean lattice. An automorphism of the Leech lattice modulo a center of two leads to the Conway group Co_1. Stabilization of the one- and two-dimensional ...

The generalized minimal residual (GMRES) method (Saad and Schultz 1986) is an extension of the minimal residual method (MINRES), which is only applicable to symmetric ...

The quaternions are members of a noncommutative division algebra first invented by William Rowan Hamilton. The idea for quaternions occurred to him while he was walking along ...