Search results
Results From The WOW.Com Content Network
When the scalar field is the real numbers, the vector space is called a real vector space, and when the scalar field is the complex numbers, the vector space is called a complex vector space. [4] These two cases are the most common ones, but vector spaces with scalars in an arbitrary field F are also commonly considered.
The state space or phase space is the geometric space in which the axes are the state variables. The system state can be represented as a vector, the state vector. If the dynamical system is linear, time-invariant, and finite-dimensional, then the differential and algebraic equations may be written in matrix form.
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 contains a subspace isomorphic to this one. The zero vector space is conceptually different from the null space of a linear operator L, which is the kernel of L.
This is a list of vector spaces in abstract mathematics, by Wikipedia page. Banach space; Besov space; Bochner space; Dual space; Euclidean space; Fock space; Fréchet space; Hardy space; Hilbert space; Hölder space; LF-space; L p space; Minkowski space; Montel space; Morrey–Campanato space; Orlicz space; Riesz space; Schwartz space; Sobolev ...
In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication.
A topological vector space homomorphism (abbreviated TVS homomorphism), also called a topological homomorphism, [2] [3] is a continuous linear map: between topological vector spaces (TVSs) such that the induced map : is an open mapping when := (), which is the range or image of , is given the subspace topology induced by .
If V is a vector space over a field K, a subset W of V is a linear subspace of V if it is a vector space over K for the operations of V.Equivalently, a linear subspace of V is a nonempty subset W such that, whenever w 1, w 2 are elements of W and α, β are elements of K, it follows that αw 1 + βw 2 is in W.
Main page; Contents; Current events; Random article; About Wikipedia; Contact us; Pages for logged out editors learn more