enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Infinite-dimensional vector function - Wikipedia

    en.wikipedia.org/wiki/Infinite-dimensional...

    An infinite-dimensional vector function is a function whose values lie in an infinite-dimensional topological vector space, such as a Hilbert space or a Banach space. Such functions are applied in most sciences including physics .

  3. Vector space - Wikipedia

    en.wikipedia.org/wiki/Vector_space

    Banach and Hilbert spaces are complete topological vector spaces whose topologies are given, respectively, by a norm and an inner product. Their study—a key piece of functional analysis—focuses on infinite-dimensional vector spaces, since all norms on finite-dimensional topological vector spaces give rise to the same notion of convergence. [71]

  4. Examples of vector spaces - Wikipedia

    en.wikipedia.org/wiki/Examples_of_vector_spaces

    The dimension of this vector space, if it exists, [a] is called the degree of the extension. For example, the complex numbers C form a two-dimensional vector space over the real numbers R. Likewise, the real numbers R form a vector space over the rational numbers Q which has (uncountably) infinite dimension, if a Hamel basis exists. [b]

  5. Basis (linear algebra) - Wikipedia

    en.wikipedia.org/wiki/Basis_(linear_algebra)

    A vector space can have several bases; however all the bases have the same number of elements, called the dimension of the vector space. This article deals mainly with finite-dimensional vector spaces. However, many of the principles are also valid for infinite-dimensional vector spaces.

  6. Dimension (vector space) - Wikipedia

    en.wikipedia.org/wiki/Dimension_(vector_space)

    For every vector space there exists a basis, [a] and all bases of a vector space have equal cardinality; [b] as a result, the dimension of a vector space is uniquely defined. We say V {\displaystyle V} is finite-dimensional if the dimension of V {\displaystyle V} is finite , and infinite-dimensional if its dimension is infinite .

  7. Linear independence - Wikipedia

    en.wikipedia.org/wiki/Linear_independence

    A vector space can be of finite dimension or infinite dimension depending on the maximum number of linearly independent vectors. The definition of linear dependence and the ability to determine whether a subset of vectors in a vector space is linearly dependent are central to determining the dimension of a vector space.

  8. Sequence space - Wikipedia

    en.wikipedia.org/wiki/Sequence_space

    In functional analysis and related areas of mathematics, a sequence space is a vector space whose elements are infinite sequences of real or complex numbers.Equivalently, it is a function space whose elements are functions from the natural numbers to the field K of real or complex numbers.

  9. Banach space - Wikipedia

    en.wikipedia.org/wiki/Banach_space

    In mathematics, more specifically in functional analysis, a Banach space (pronounced ) is a complete normed vector space.Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vectors and is complete in the sense that a Cauchy sequence of vectors always converges to a well-defined limit that is within the space.