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...efer to one of several operations between two (or more) [[Euclidean vector|vectors]]. It may concern any of the following articles: ...s the product of the projection of the first vector onto the second vector and the magnitude of the second vector. Thus, <math display=block>\mathbf{a} \c ...

...'primordial element''' is a particular kind of a [[Vector (mathematics and physics)|vector]] in a [[vector space]]. ...ndexed family|<math>I</math>-indexed]] [[Basis (linear algebra)|basis]] of vectors for <math>V.</math> ...

[[File:Sylvester theorem1.svg|thumb|upright=1.5|sum of three equal lengthed vectors]] ...n of the sum of three pairwise distinct [[vector (mathematics and physics)|vectors]] of equal length in the context of [[triangle geometry]]. It is also refer ...

...tors are a methodology of [[software testing]] and [[software verification and validation]]. ...<math>X</math> is an input vector. While testing the system, various test vectors must be used to examine the system's behavior with differing inputs. ...

...nts of some [[vector space]]s. They have to be expressed by both magnitude and direction. ...nted by [[geometric vector]]s in the same way as [[distance]]s, [[mass]]es and [[time]] are represented by [[real number]]s. ...

...d to describe this process in a manner analogous to "summatory" (for sums) and "productory" (for products). Here, <math>\otimes</math> denotes the tensor product operator, and the result is a higher-dimensional tensor whose rank is the sum of the rank ...

...arallel to each facet of the two given polytopes, with the same [[Measure (mathematics)|measure]]. When both polytopes have parallel facets, the measure of the co ...y can be used to decompose arbitrary polytopes into [[simplex|simplices]], and [[central symmetry|centrally symmetric]] polytopes into [[Parallelohedron#P ...

In [[mathematics]], a '''universal geometric algebra''' is a type of [[geometric algebra]] g ...metric algebra|geometric product]]. This product makes the manipulation of vectors more similar to the familiar algebraic rules, although non-[[abelian algebr ...

..._s)_{s\in S}</math> such that <math>x_s = 1</math> if <math>s \in T</math> and <math>x_s = 0</math> if <math>s \notin T.</math> ..._2,\ldots,x_n)</math> where <math>x_i = 1</math> if <math>s_i \in T</math> and <math>x_i = 0</math> if <math>s_i \notin T.</math> ...

.../math> asymmetric vectors. As each vector can be characterized by its norm and phase, variations in the <math>M^2</math> amplitudes can modify the respect ...rn analysis in physics and environmental sciences operating on time-series and digital images. ...

...ions of a dynamical system. They have been used in predictability analysis and as initial perturbations for [[ensemble forecasting]] in [[numerical weathe ...by a d-dimensional state vector <math>x\in\mathbb{R}^d</math> the Lyapunov vectors <math>v^{(k)}(x)</math>, <math>(k=1\dots d)</math> point in the directions ...

...:Eutactic star 3D.png|thumb|right|A eutactic star consisting of 5 pairs of vectors in three-dimensional space (''n''&nbsp;=&nbsp;3, ''s''&nbsp;=&nbsp;5)]] ...34}} because, for a common [[Scalar (mathematics)|scalar multiple]], their vectors are projections of an [[orthonormal basis]].<ref>{{cite book|title=Eigenspa ...

{{Short description|Exterior product of vectors}} ...d as the [[exterior product]] (informally ''wedge product'') of 1-vectors, and is of ''[[Graded algebra|grade]]'' {{math|''k''}}. ...

...specification of the shape of a polytope by the directions and [[Measure (mathematics)|measures]] of its [[Facet (geometry)|facets]].{{r|klain}} The theorem that ==Specification and necessary conditions== ...

...ly relates to the description of [[angular momentum]] in quantum mechanics and [[spherical harmonic]] functions. ...distance, the spherical basis are constructed from the [[standard basis]] and use [[complex number]]s. ...

{{short description|Formulas about vectors in three-dimensional Euclidean space}} ...ere.{{refn|group=nb|There is also a [[seven-dimensional cross product]] of vectors that relates to multiplication in the [[octonion]]s, but it does not satisf ...

...om the center of this isotropic vector field are uniformly, symmetrically, and invariantly spread across space.]] ...is implies that the vector field does not prefer any particular direction, and its characteristics are invariant under rotations about any point. ...

...171 [http://mcl1.ncifcrf.gov/dauter_pubs/284.pdf pdf]</ref> Direct lattice vectors have components measured in distance units, like [[Metre|meters]] (m) or [[ ...ne|1}}00], [0{{overline|1}}0] and [00{{overline|1}}] because each of these vectors is symmetrically equivalent under a 90 degree rotation along an axis. A bar ...

for all vectors <math>x</math> and all multivectors <math>A</math> and <math>B</math>, where <math>\textstyle \bigwedge(V)</math> denotes the [[ex ...ample, we see that for scalars <math>\alpha</math>, <math>\beta</math> and vectors <math>x</math>, <math>y</math>, <math>z</math>, the outermorphism is linear ...

...athematics]], the '''Chung–Fuchs theorem''', named after [[Chung Kai-lai]] and [[Wolfgang Heinrich Johannes Fuchs]], states that for a particle undergoing where <math>Z_1, Z_2, \dots, Z_n</math> are independent m-dimensional vectors with a given multivariate distribution, ...