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A point is a 0-dimensional mathematical object which can be specified in n-dimensional space using an n-tuple (x_1, x_2, ..., x_n) consisting of n coordinates. In dimensions ...

The solid angle Omega subtended by a surface S is defined as the surface area Omega of a unit sphere covered by the surface's projection onto the sphere. This can be written ...

A transition function describes the difference in the way an object is described in two separate, overlapping coordinate charts, where the description of the same set may ...

A triangle is a 3-sided polygon sometimes (but not very commonly) called the trigon. Every triangle has three sides and three angles, some of which may be the same. The sides ...

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 ...

A Hermitian form on a vector space V over the complex field C is a function f:V×V->C such that for all u,v,w in V and all a,b in R, 1. f(au+bv,w)=af(u,w)+bf(v,w). 2. ...

In a set X equipped with a binary operation · called a product, the multiplicative identity is an element e such that e·x=x·e=x for all x in X. It can be, for example, the ...

An orthogonal transformation is a linear transformation T:V->V which preserves a symmetric inner product. In particular, an orthogonal transformation (technically, an ...

If W is a k-dimensional subspace of a vector space V with inner product <,>, then it is possible to project vectors from V to W. The most familiar projection is when W is the ...

A walk is a sequence v_0, e_1, v_1, ..., v_k of graph vertices v_i and graph edges e_i such that for 1<=i<=k, the edge e_i has endpoints v_(i-1) and v_i (West 2000, p. 20). ...