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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.
This is an accepted version of this page This is the latest accepted revision, reviewed on 28 January 2025. Computer graphics images defined by points, lines and curves This article is about computer illustration. For other uses, see Vector graphics (disambiguation). Example showing comparison of vector graphics and raster graphics upon magnification Vector graphics are a form of computer ...
In the natural sciences, a vector quantity (also known as a vector physical quantity, physical vector, or simply vector) is a vector-valued physical quantity. [9] [10] It is typically formulated as the product of a unit of measurement and a vector numerical value (), often a Euclidean vector with magnitude and direction.
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in ^ (pronounced "v-hat").
In linear algebra, a column vector with elements is an matrix [1] consisting of a single column of entries, for example, = [].. Similarly, a row vector is a matrix for some , consisting of a single row of entries, = […]. (Throughout this article, boldface is used for both row and column vectors.)
In this article, vectors are represented in boldface to distinguish them from scalars. [nb 1] [1]A vector space over a field F is a non-empty set V together with a binary operation and a binary function that satisfy the eight axioms listed below.
A four-vector A is a vector with a "timelike" component and three "spacelike" components, and can be written in various equivalent notations: [3] = (,,,) = + + + = + = where A α is the magnitude component and E α is the basis vector component; note that both are necessary to make a vector, and that when A α is seen alone, it refers strictly to the components of the vector.
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