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In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, can be added together and multiplied ("scaled") by numbers called scalars. Scalars are often real numbers, but can be complex numbers or, more generally, elements of any field. The operations of vector addition and scalar ...
Euclidean 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. Euclidean vectors can be added and scaled to form a vector space.
Inkscape. Inkscape is a free and open-source vector graphics editor for traditional Unix-compatible systems such as GNU / Linux, BSD derivatives and Illumos, as well as Windows and macOS. It offers a rich set of features and is widely used for both artistic and technical illustrations such as cartoons, clip art, logos, typography, diagramming ...
Category. v. t. e. In mechanics, a couple is a system of forces with a resultant (a.k.a. net or sum) moment of force but no resultant force. [1] A more descriptive term is force couple or pure moment. Its effect is to impart angular momentum but no linear momentum. In rigid body dynamics, force couples are free vectors, meaning their effects on ...
Vector space. Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is stretched by a factor of 2, yielding the sum v + 2w. In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, can be added together and ...
Eigenvalues and eigenvectors. In linear algebra, an eigenvector ( / ˈaɪɡən -/ EYE-gən-) or characteristic vector is a vector that has its direction unchanged by a given linear transformation. More precisely, an eigenvector, , of a linear transformation, , is scaled by a constant factor, , when the linear transformation is applied to it: .
Vector field. In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space . [1] A vector field on a plane can be visualized as a collection of arrows with given magnitudes and directions, each attached to a point on the plane. Vector fields are often used to model, for ...
Vector notation. Describing an arrow vector v by its coordinates x and y yields an isomorphism of vector spaces. 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 .
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