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Let f be a function defined on a set A and taking values in a set B. Then f is said to be a surjection (or surjective map) if, for any b in B, there exists an a in A for ...

In simple terms, let x, y, and z be members of an algebra. Then the algebra is said to be associative if x·(y·z)=(x·y)·z, (1) where · denotes multiplication. More formally, ...

In n-dimensional Lorentzian space R^n=R^(1,n-1), the light cone C^(n-1) is defined to be the subset consisting of all vectors x=(x_0,x_1,...,x_(n-1)) (1) whose squared ...

The Siegel theta function is a Gamma_n-invariant meromorphic function on the space of all p×p symmetric complex matrices Z=X+iY with positive definite imaginary part. It is ...

A number of areas of mathematics have the notion of a "dual" which can be applies to objects of that particular area. Whenever an object A has the property that it is equal ...

A seminorm is a function on a vector space V, denoted ||v||, such that the following conditions hold for all v and w in V, and any scalar c. 1. ||v||>=0, 2. ||cv||=|c|||v||, ...

Given a complex Hilbert space H with associated space L(H) of continuous linear operators from H to itself, the commutant M^' of an arbitrary subset M subset= L(H) is the ...

Suppose that V is a group representation of G, and W is a group representation of H. Then the vector space tensor product V tensor W is a group representation of the group ...

CP.

The Gauss map is a function N from an oriented surface M in Euclidean space R^3 to the unit sphere in R^3. It associates to every point on the surface its oriented unit ...