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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]
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 ...
The Shapley–Folkman lemma is illustrated by the Minkowski addition of four sets. The point (+) in the convex hull of the Minkowski sum of the four non-convex sets (right) is the sum of four points (+) from the (left-hand) sets—two points in two non-convex sets plus two points in the convex hulls of two sets.
In mathematics, vector algebra may mean: The operations of vector addition and scalar multiplication of a vector space; The algebraic operations in vector calculus (vector analysis) – including the dot and cross products of 3-dimensional Euclidean space; Algebra over a field – a vector space equipped with a bilinear product
Vectorial addition chains are well suited to perform multi-exponentiation: [1] Input: Elements x 0,...,x k-1 of an abelian group G and a vectorial addition chain of dimension k computing [n 0,...,n k-1] Output:The element x 0 n 0...x k-1 n r-1. for i =-k+1 to 0 do y i → x i+k-1; for i = 1 to s do y i →y j ×y r; return y s
Euclidean vector#Addition and subtraction To a section : This is a redirect from a topic that does not have its own page to a section of a page on the subject. For redirects to embedded anchors on a page, use {{ R to anchor }} instead .