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infinite-dimensional vector

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  • Infinite-dimensional holomorphy — In mathematics, infinite dimensional holomorphy is a branch of functional analysis. It is concerned with generalizations of the concept of holomorphic function to functions defined and taking values in complex Banach spaces (or Fréchet spaces… …   Wikipedia

  • Infinite-dimensional optimization — In certain optimization problems the unknown optimal solution might be not a number or a vector, but rather a continuous quantity, for example a function or the shape of a body. Such a problem is an infinite dimensional optimization problem,… …   Wikipedia

  • Fixed point theorems in infinite-dimensional spaces — In mathematics, a number of fixed point theorems in infinite dimensional spaces generalise the Brouwer fixed point theorem. They have applications, for example, to the proof of existence theorems for partial differential equations. The first… …   Wikipedia

  • Fixed-point theorems in infinite-dimensional spaces — In mathematics, a number of fixed point theorems in infinite dimensional spaces generalise the Brouwer fixed point theorem. They have applications, for example, to the proof of existence theorems for partial differential equations. The first… …   Wikipedia

  • Vector space — This article is about linear (vector) spaces. For the structure in incidence geometry, see Linear space (geometry). Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is… …   Wikipedia

  • Examples of vector spaces — This page lists some examples of vector spaces. See vector space for the definitions of terms used on this page. See also: dimension, basis. Notation . We will let F denote an arbitrary field such as the real numbers R or the complex numbers C.… …   Wikipedia

  • Coordinate vector — In linear algebra, a coordinate vector is an explicit representation of a vector in an abstract vector space as an ordered list of numbers or, equivalently, as an element of the coordinate space Fn. Coordinate vectors allow calculations with… …   Wikipedia

  • Normed vector space — In mathematics, with 2 or 3 dimensional vectors with real valued entries, the idea of the length of a vector is intuitive and can easily be extended to any real vector space Rn. The following properties of vector length are crucial. 1. The zero… …   Wikipedia

  • Dimension (vector space) — In mathematics, the dimension of a vector space V is the cardinality (i.e. the number of vectors) of a basis of V. It is sometimes called Hamel dimension or algebraic dimension to distinguish it from other types of dimension. This description… …   Wikipedia

  • Support vector machine — Support vector machines (SVMs) are a set of related supervised learning methods used for classification and regression. Viewing input data as two sets of vectors in an n dimensional space, an SVM will construct a separating hyperplane in that… …   Wikipedia

  • Topological vector space — In mathematics, a topological vector space is one of the basic structures investigated in functional analysis. As the name suggests the space blends a topological structure (a uniform structure to be precise) with the algebraic concept of a… …   Wikipedia

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