Search results
Results From The WOW.Com Content Network
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 free vector is a vector quantity having an undefined support or region of application; it can be freely translated with no consequences; a displacement vector is a prototypical example of free vector. Aside from the notion of units and support, physical vector quantities may also differ from Euclidean vectors in terms of metric.
More generally, field extensions provide another class of examples of vector spaces, particularly in algebra and algebraic number theory: a field F containing a smaller field E is an E-vector space, by the given multiplication and addition operations of F. [34]
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 topological vector space (TVS) , such as a Banach space, is said to be a topological direct sum of two vector subspaces and if the addition map (,) + is an isomorphism of topological vector spaces (meaning that this linear map is a bijective homeomorphism), in which case and are said to be topological complements in .
Like a vector space, a module is an additive abelian group, and scalar multiplication is distributive over the operations of addition between elements of the ring or module and is compatible with the ring multiplication. Modules are very closely related to the representation theory of groups.
The simplest example of a vector space is the trivial one: {0}, which contains only the zero vector (see the third axiom in the Vector space article). Both vector addition and scalar multiplication are trivial. A basis for this vector space is the empty set, so that {0} is the 0-dimensional vector space over F. Every vector space over F ...
Another example of a coset comes from the theory of vector spaces. The elements (vectors) of a vector space form an abelian group under vector addition. The subspaces of the vector space are subgroups of this group.