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A convex polyhedron can be defined algebraically as the set of solutions to a system of linear inequalities mx<=b, where m is a real s×3 matrix and b is a real s-vector. ...

A branch of mathematics which brings together ideas from algebraic geometry, linear algebra, and number theory. In general, there are two main types of K-theory: topological ...

A real polynomial P is said to be stable if all its roots lie in the left half-plane. The term "stable" is used to describe such a polynomial because, in the theory of linear ...

A relation connecting the values of a meromorphic function inside a disk with its boundary values on the circumference and with its zeros and poles (Jensen 1899, Levin 1980). ...

If a function has a Fourier series given by f(x)=1/2a_0+sum_(n=1)^inftya_ncos(nx)+sum_(n=1)^inftyb_nsin(nx), (1) then Bessel's inequality becomes an equality known as ...

A weighted adjacency matrix A_f of a simple graph is defined for a real positive symmetric function f(d_i,d_j) on the vertex degrees d_i of a graph as ...

The inverse tangent is the multivalued function tan^(-1)z (Zwillinger 1995, p. 465), also denoted arctanz (Abramowitz and Stegun 1972, p. 79; Harris and Stocker 1998, p. 311; ...

Let ||f|| be the supremum of |f(x)|, a real-valued function f defined on (0,infty). If f is twice differentiable and both f and f^('') are bounded, Landau (1913) showed that ...

Gram-Schmidt orthogonalization, also called the Gram-Schmidt process, is a procedure which takes a nonorthogonal set of linearly independent functions and constructs an ...

A global maximum, also known as an absolute maximum, the largest overall value of a set, function, etc., over its entire range. It is impossible to construct an algorithm ...