Search Results for ""

A vector whose elements are real numbers.

Roughly speaking, a tangent vector is an infinitesimal displacement at a specific point on a manifold. The set of tangent vectors at a point P forms a vector space called the ...

The product of a family {X_i}_(i in I) of objects of a category is an object P=product_(i in I)X_i, together with a family of morphisms {p_i:P->X_i}_(i in I) such that for ...

The normalized vector of X is a vector in the same direction but with norm (length) 1. It is denoted X^^ and given by X^^=(X)/(|X|), where |X| is the norm of X. It is also ...

A vector bundle is special class of fiber bundle in which the fiber is a vector space V. Technically, a little more is required; namely, if f:E->B is a bundle with fiber R^n, ...

The wedge product is the product in an exterior algebra. If alpha and beta are differential k-forms of degrees p and q, respectively, then alpha ^ beta=(-1)^(pq)beta ^ alpha. ...

In the Minkowski space of special relativity, a four-vector is a four-element vector x^mu=(x^0,x^1,x^2,x^3) that transforms under a Lorentz transformation like the position ...

A vector sum is the result of adding two or more vectors together via vector addition. It is denoted using the normal plus sign, i.e., the vector sum of vectors A, B, and C ...

A function A such that B=del xA. The most common use of a vector potential is the representation of a magnetic field. If a vector field has zero divergence, it may be ...

The Cartesian product of two sets A and B (also called the product set, set direct product, or cross product) is defined to be the set of all points (a,b) where a in A and b ...