physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has...

associated vector space is a Euclidean vector space. Euclidean spaces are sometimes called Euclidean affine spaces to distinguish them from Euclidean vector spaces...

operations on the above sorts of vectors. A vector space formed by geometric vectors is called a Euclidean vector space, and a vector space formed by tuples is...

applied as the measure of units between a number and zero. In vector spaces, the Euclidean norm is a measure of magnitude used to define a distance between...

particular, the Euclidean distance in a Euclidean space is defined by a norm on the associated Euclidean vector space, called the Euclidean norm, the 2-norm...

(usually coordinate vectors), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used...

Look up vector or vectorial in Wiktionary, the free dictionary. Vector most often refers to: Euclidean vector, a quantity with a magnitude and a direction...

origin' of the vector space. Euclidean spaces are sometimes called Euclidean affine spaces for distinguishing them from Euclidean vector spaces. This is...

combinatorics. In geometry, two Euclidean vectors are orthogonal if they are perpendicular, i.e. they form a right angle. Two vectors u and v in an inner product...

measurement and a vector numerical value (unitless), often a Euclidean vector with magnitude and direction. For example, a position vector in physical space...

In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space R n {\displaystyle...

+(p_{n}-q_{n})^{2}}}.} The Euclidean distance may also be expressed more compactly in terms of the Euclidean norm of the Euclidean vector difference: d ( p ,...

inner product of a vector and itself. The Euclidean norm of a Euclidean vector space is a special case that allows defining Euclidean distance by the formula...

so that ei + ej is a null vector. In a pseudo-Euclidean space with k < n, unlike in a Euclidean space, there exist vectors with negative scalar square...

linear algebra and calculus to be generalized from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise...

Vector notation In mathematics and physics, vector notation is a commonly used notation for representing vectors, which may be Euclidean vectors, or more...

angles, and orthogonality (zero inner product) of vectors. Inner product spaces generalize Euclidean vector spaces, in which the inner product is the dot...

In mathematics, a Euclidean plane is a Euclidean space of dimension two, denoted E 2 {\displaystyle {\textbf {E}}^{2}} or E 2 {\displaystyle \mathbb {E}...

relaxed. Every tangent space of a pseudo-Riemannian manifold is a pseudo-Euclidean vector space. A special case used in general relativity is a four-dimensional...

and a unit vector for the axis, or as a Euclidean vector obtained by multiplying the angle with this unit vector, called the rotation vector (although...

In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents a point P in space....

(also called Euclidean transformation or Euclidean isometry) is a geometric transformation of a Euclidean space that preserves the Euclidean distance between...

a nonzero null vector. A quadratic space (X, q) which has a null vector is called a pseudo-Euclidean space. The term isotropic vector v when q(v) = 0...

definition of Euclidean space implied by Euclid's Elements, for convenience most modern sources define affine spaces in terms of the well developed vector space...

fields, primarily in three-dimensional Euclidean space, R 3 . {\displaystyle \mathbb {R} ^{3}.} The term vector calculus is sometimes used as a synonym...

a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here E {\displaystyle E} ), and is denoted by the symbol...

Scalars can also be, more generally, elements of any field. Vector spaces generalize Euclidean vectors, which allow modeling of physical quantities (such as...

Lorentz group, the (⁠1/2⁠,⁠1/2⁠) representation. It differs from a Euclidean vector in how its magnitude is determined. The transformations that preserve...

differently from a symmetric form, for example, the scalar product on Euclidean vector spaces. The standard symplectic space is R 2 n {\displaystyle \mathbb...

complex number-based vector space that can be associated with Euclidean space. A spinor transforms linearly when the Euclidean space is subjected to...