nonzero vector
1Vector space — This article is about linear (vector) spaces. For the structure in incidence geometry, see Linear space (geometry). Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is… …
2Nonzero-rule — A curve (top) is filled according to two rules: the even odd rule (left), and the non zero winding rule (right). In each case an arrow shows a ray from a point P heading out of the curve. In the even odd case, the ray is intersected by two lines …
3Direction vector — In mathematics, a direction vector that describes a line segment D is any vector where A and B are two distinct points on the line D. If v is a direction vector for D, so is kv for any nonzero scalar k; and these are in fact all of the direction… …
4Examples of vector spaces — This page lists some examples of vector spaces. See vector space for the definitions of terms used on this page. See also: dimension, basis. Notation . We will let F denote an arbitrary field such as the real numbers R or the complex numbers C.… …
5Coordinate vector — In linear algebra, a coordinate vector is an explicit representation of a vector in an abstract vector space as an ordered list of numbers or, equivalently, as an element of the coordinate space Fn. Coordinate vectors allow calculations with… …
6Super vector space — In mathematics, a super vector space is another name for a Z2 graded vector space, that is, a vector space over a field K with a given decomposition:V=V 0oplus V 1.The study of super vector spaces and their generalizations is sometimes called… …
7Orientation (vector space) — See also: orientation (geometry) The left handed orientation is shown on the left, and the right handed on the right. In mathematics, orientation is a notion that in two dimensions allows one to say when a cycle goes around clockwise or… …
8Symplectic vector space — In mathematics, a symplectic vector space is a vector space V equipped with a nondegenerate, skew symmetric, bilinear form omega; called the symplectic form. Explicitly, a symplectic form is a bilinear form omega; : V times; V rarr; R which is *… …
9Killing vector field — In mathematics, a Killing vector field, named after Wilhelm Killing, is a vector field on a Riemannian manifold (or pseudo Riemannian manifold) that preserves the metric. Killing fields are the infinitesimal generators of isometries; that is,… …
10Dimension theorem for vector spaces — In mathematics, the dimension theorem for vector spaces states that all bases of a vector space have equally many elements. This number of elements may be finite, or given by an infinite cardinal number, and defines the dimension of the space.… …
