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A method for finding solutions u and v to a linear congruence au+bv=d by constructing a matrix formed by adjoining a vector containing a and b with a unit matrix, M=[a 1 0; b ...

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 ...

Let A denote an R-algebra, so that A is a vector space over R and A×A->A (1) (x,y)|->x·y. (2) Now define Z={x in A:x·y=0 for some y in A!=0}, (3) where 0 in Z. An Associative ...

A complete metric space is a metric space in which every Cauchy sequence is convergent. Examples include the real numbers with the usual metric, the complex numbers, ...

Differential entropy differs from normal or absolute entropy in that the random variable need not be discrete. Given a continuous random variable X with a probability density ...

The term endomorphism derives from the Greek adverb endon ("inside") and morphosis ("to form" or "to shape"). In algebra, an endomorphism of a group, module, ring, vector ...

In real and functional analysis, equicontinuity is a concept which extends the notion of uniform continuity from a single function to collection of functions. Given ...

An evolute is the locus of centers of curvature (the envelope) of a plane curve's normals. The original curve is then said to be the involute of its evolute. Given a plane ...

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 ...

An extreme point of a subset K of a vector space X is an extreme set S of K which consists of a single point x in K. The collection of all extreme points of K is sometimes ...