# Vector (mathematics and physics)

**vectorvectorsvectorialvectors (mathematics and physics)vectors in mathematics and physics**

In mathematics and physics, a vector is an element of a vector space.wikipedia

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### Ordered pair

**ordered pairspairpairs**

In classical Euclidean geometry (that is in synthetic geometry), vectors were introduced (during 19th century) as equivalence classes, under equipollence, of ordered pairs of points; two pairs

Ordered pairs are also called 2-tuples, or sequences (sometimes, lists in a computer science context) of length 2; ordered pairs of scalars are also called 2-dimensional vectors.

### Dot product

**scalar productdotinner product**

In this case, a Euclidean vector is an element of a normed vector space of finite dimension over the reals, or, typically, an element of \mathbb R^n equipped with the dot product.

In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used and often called "the" inner product (or rarely projection product) of Euclidean space even though it is not the only inner product that can be defined on Euclidean space; see also inner product space.

### Norm (mathematics)

**normEuclidean normseminorm**

In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—except for the zero vector, which is assigned a length of zero.

### Tuple

**tuplesn-tuple5-tuple**

This defines Cartesian coordinates of any point P of the space, as the coordinates on this basis of the vector These choices define an isomorphism of the given Euclidean space onto by mapping any point to the n-tuple of its Cartesian coordinates, and every vector to its coordinate vector.

The term tuple can often occur when discussing other mathematical objects, such as vectors.

### Normal (geometry)

**normalnormal vectorsurface normal**

In geometry, a normal is an object such as a line or vector that is perpendicular to a given object.

### Gradient

**gradientsgradient vectorvector gradient**

of several variables, is the vector field, or more simply a vector-valued function, whose value at a point p is the vector whose components are the partial derivatives of f at p:

### Function of several real variables

**functions of several real variablesReal multivariable functionmulti-variable function**

by using a notation similar to that for vectors, like boldface

### Vector space

**vectorvector spacesvectors**

In mathematics and physics, a vector is an element of a vector space.

*Vector (mathematics and physics), for a list of various kinds of vectors

### Orientability

**orientableorientednon-orientable**

In mathematics, orientability is a property of surfaces in Euclidean space that measures whether it is possible to make a consistent choice of surface normal vector at every point.

### Ricci calculus

**tensor index notationabsolute differential calculusantisymmetrization of indices**

A tensor may be expressed as a linear sum of the tensor product of vector and covector basis elements.

### Function (mathematics)

**functionfunctionsmathematical function**

For example, in linear algebra and functional analysis, linear forms and the vectors they act upon are denoted using a dual pair to show the underlying duality.

### Vector

**Vector (disambiguation)**

* Vector (disambiguation)

### Vector notation

**notation**

It must be emphasized that a polar vector is not really a vector, since the addition of two polar vectors is not defined.

### Mathematics

**mathematicalmathmathematician**

In mathematics and physics, a vector is an element of a vector space.

### Physics

**physicistphysicalphysicists**

In mathematics and physics, a vector is an element of a vector space.

### Geometry

**geometricgeometricalgeometries**

Historically, vectors were introduced in geometry and physics (typically in mechanics) before the formalization of the concept of vector space.

### Mechanics

**mechanicaltheoretical mechanicsmechanician**

Historically, vectors were introduced in geometry and physics (typically in mechanics) before the formalization of the concept of vector space.

### Scalar multiplication

**multipliedmultiplicationscalar multiple**

Specifically, in a Euclidean space, one considers spatial vectors, also called Euclidean vectors which are used to represent quantities that have both magnitude and direction, and may be added and scaled (that is multiplied by a real number) for forming a vector space.

### Real number

**realrealsreal-valued**

Specifically, in a Euclidean space, one considers spatial vectors, also called Euclidean vectors which are used to represent quantities that have both magnitude and direction, and may be added and scaled (that is multiplied by a real number) for forming a vector space.

### Euclidean geometry

**plane geometryEuclideanEuclidean plane geometry**

In classical Euclidean geometry (that is in synthetic geometry), vectors were introduced (during 19th century) as equivalence classes, under equipollence, of ordered pairs of points; two pairs

### Synthetic geometry

**syntheticpure geometrysynthetic geometer**

In classical Euclidean geometry (that is in synthetic geometry), vectors were introduced (during 19th century) as equivalence classes, under equipollence, of ordered pairs of points; two pairs

### Equivalence class

**quotient setequivalence classesquotient**

### Equipollence (geometry)

**equipollenceequipollentequipollence class**

### Parallelogram

**parallelogramsparallelogram linkages**

, in this order, form a parallelogram.

### Euclidean vector

**vectorvectorsvector addition**

Specifically, in a Euclidean space, one considers spatial vectors, also called Euclidean vectors which are used to represent quantities that have both magnitude and direction, and may be added and scaled (that is multiplied by a real number) for forming a vector space.