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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: ...magnitudes of the two vectors and the cosine of the angle between the two vectors. Alternatively, it is defined as the product of the projection of the first ...

Historically, vectors were introduced in [[geometry]] and physics (typically in [[mechanics]]) fo ...erations 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 ...

Thus, the order of operations in a tensotory does not affect the result. === Example 1: Simple Tensotory of Vectors === ...

...e index set of a family induces an ordering on the family, but no ordering on the corresponding image set. ===Indexed vectors=== ...

...ex bodies, generalizing both the polytope and smooth cases, using measures on the [[Gauss map]].{{r|grun2}} ...ue shape, in the sense that any two polytopes described by the same set of vectors are [[Translation (geometry)|translates]] of each other.{{r|grunbaum}} ...

=== ''n'' vectors in ''n''-dimensional space === ...s<ref>{{cite journal| doi=10.1016/j.jat.2008.03.005 | volume=156 | title= On d-dimensional d-semimetrics and simplex-type inequalities for high-dimensio ...

...metric algebra|geometric product]]. This product makes the manipulation of vectors more similar to the familiar algebraic rules, although non-[[abelian algebr ...re [[scalar (mathematics)|scalars]] ({{math|1=''r'' = 0}}), [[vector space|vectors]] ({{math|1=''r'' = 1}}) and [[bivector]]s ({{math|1=''r'' = 2}}). ...

'''Tensor product''' refers to one of several related binary operations, typically denoted <math>- \otimes -</math>. Usually, they are [[Associativ * [[Tensor product|Tensor product of vector spaces]], an operation on [[Vector space|vector spaces]] (the original tensor product) ...

{{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 ...

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

...he underlying space of the point process into another space. Point process operations and the resulting point processes are used in the theory of [[point process ...on is applied to some Poisson point process, then provided some conditions on the point process operation, the resulting process will be often another Po ...

...t the [[computer hardware|hardware]] level (i.e. without programming these operations).<ref name="Malinovsky">{{cite book |last= Malinovsky |first=B.N. |title= T ...with functions are performed as unique computer operations with such codes on a "single" [[arithmetic logic unit|arithmetic unit]].<ref name="Khmelnik2" ...

...</ref><ref>{{Cite journal|last=Yager|first=Ronald R.|date=1997-10-01|title=On the analytic representation of the Leximin ordering and its application to * The smallest elements of both vectors are equal, and the second-smallest element of '''x''' is larger than the se ...

...bility density function''' is a class of [[probability density function]]s on the real line. The class contains the density functions of all distribution ...[[Characteristic function (probability theory)|characteristic function]]. On either <math>[0, +\infty)</math> or <math>(-\infty, 0)</math> these probabi ...

...). The Application of Vector Theory to Syllogistic Logic. New Perspectives on the Square of Opposition, Bern, Peter Lang.</ref> In the vector space for p ...]] logic is represented by a small set of mathematical functions depending on one (monadic) or two (dyadic) variables. In the binary set, the value 1 cor ...

...n algebraic combinatorics)|ring of symmetric functions|symmetric functions on elements of a vector space |symmetric tensor}} ...hic]] to the space of [[homogeneous polynomials]] of degree <math>k</math> on <math>V.</math> Symmetric functions should not be confused with [[even and ...

...tity for vector addition {{math|'''0'''}}, so these must be omitted or all vectors will be identified.}} ...|∞}} can be interpreted as either positive or negative infinity, depending on convention.}} so it is clearer to write this using the extended real number ...

...hat finding collisions in SWIFFT is at least as difficult as finding short vectors in cyclic/[[Ideal lattice cryptography|ideal lattices]] in the ''worst case ...ions, the algorithm is quite fast, yielding a throughput of 40&nbsp;Mbit/s on a 3.2&nbsp;GHz Intel Pentium 4. Although SWIFFT satisfies many desirable cr ...

...ed on matrices (such as [[matrix addition]], [[matrix multiplication]] and operations derived from these), functions of matrices (such as [[matrix exponentiation Since matrices form vector spaces, one can form axioms (analogous to those of vectors) to define a "size" of a particular matrix. The norm of a matrix is a posit ...

...nerally, items) as [[vector space|vectors]] such that the distance between vectors represents the relevance between the documents. It is used in [[information ...el|bag-of-words]] representation. Documents and queries are represented as vectors. ...