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For Minkowski addition, the zero set, {}, containing only the zero vector, 0, is an identity element: for every subset S of a vector space, S + { 0 } = S . {\displaystyle S+\{0\}=S.} The empty set is important in Minkowski addition, because the empty set annihilates every other subset: for every subset S of a vector space, its sum with the ...
An addition sequence for the set of integer S ={n 0, ..., n r-1} is an addition chain v that contains every element of S. For example, an addition sequence computing {47,117,343,499}
A vector addition system (VAS) is one of several mathematical modeling languages for the description of distributed systems.Vector addition systems were introduced by Richard M. Karp and Raymond E. Miller in 1969, [1] and generalized to vector addition systems with states (VASS) by John E. Hopcroft and Jean-Jacques Pansiot in 1979. [2]
A vector measure is a vector-valued generalization of a measure; for example, if p 1 and p 2 are probability measures defined on the same measurable space, then the product function p 1 p 2 is a vector measure, where p 1 p 2 is defined for every event ω by (p 1 p 2)(ω)=(p 1 (ω), p 2 (ω)).
Basic Linear Algebra Subprograms (BLAS) is a specification that prescribes a set of low-level routines for performing common linear algebra operations such as vector addition, scalar multiplication, dot products, linear combinations, and matrix multiplication.
In mathematics, a geometric algebra (also known as a Clifford algebra) is an algebra that can represent and manipulate geometrical objects such as vectors.Geometric algebra is built out of two fundamental operations, addition and the geometric product.
The following are important identities in vector algebra.Identities that only involve the magnitude of a vector ‖ ‖ and the dot product (scalar product) of two vectors A·B, apply to vectors in any dimension, while identities that use the cross product (vector product) A×B only apply in three dimensions, since the cross product is only defined there.
A vector space over a field F (often the field of the real numbers) is a set V equipped with two binary operations. Elements of V are called vectors, and elements of F are called scalars. The first operation, vector addition, takes any two vectors v and w and outputs a third vector v + w.
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