Search results
Results from the WOW.Com Content Network
Ordered pairs of scalars are sometimes called 2-dimensional vectors. (Technically, this is an abuse of terminology since an ordered pair need not be an element of a vector space.) The entries of an ordered pair can be other ordered pairs, enabling the recursive definition of ordered n-tuples (ordered lists of n objects).
A two-vector or bivector [1] is a tensor of type () and it is the dual of a two-form, meaning that it is a linear functional which maps two-forms to the real numbers (or more generally, to scalars). The tensor product of a pair of vectors is a two-vector.
A vector pointing from A to B. In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector [1] or spatial vector [2]) is a geometric object that has magnitude (or length) and direction.
The term cycle may also refer to an element of the cycle space of a graph. There are many cycle spaces, one for each coefficient field or ring. The most common is the binary cycle space (usually called simply the cycle space), which consists of the edge sets that have even degree at every vertex; it forms a vector space over the two-element field.
Given a vector at the north pole, one can transport this vector along a curve by rotating the sphere in such a way that the north pole moves along the curve without axial rolling. This latter means of parallel transport is the Levi-Civita connection on the sphere.
An equivalent definition of a vector space can be given, which is much more concise but less elementary: the first four axioms (related to vector addition) say that a vector space is an abelian group under addition, and the four remaining axioms (related to the scalar multiplication) say that this operation defines a ring homomorphism from the ...
In combinatorics, a branch of mathematics, a matroid / ˈ m eɪ t r ɔɪ d / is a structure that abstracts and generalizes the notion of linear independence in vector spaces.There are many equivalent ways to define a matroid axiomatically, the most significant being in terms of: independent sets; bases or circuits; rank functions; closure operators; and closed sets or flats.
In mathematics and physics, vector notation is a commonly used notation for representing vectors, [1] [2] which may be Euclidean vectors, or more generally, members of a vector space. For denoting a vector, the common typographic convention is lower case, upright boldface type, as in v .