### What does **dual space** mean?

# Definitions for dual space

du·al space

#### This dictionary definitions page includes all the possible meanings, example usage and translations of the word **dual space**.

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### Wiktionary

dual spacenoun

The vector space which comprises the set of linear transformations of a given vector space into its scalar field

### Wikipedia

Dual space

In mathematics, any vector space V {\displaystyle V} has a corresponding dual vector space (or just dual space for short) consisting of all linear forms on V {\displaystyle V} , together with the vector space structure of pointwise addition and scalar multiplication by constants. The dual space as defined above is defined for all vector spaces, and to avoid ambiguity may also be called the algebraic dual space. When defined for a topological vector space, there is a subspace of the dual space, corresponding to continuous linear functionals, called the continuous dual space. Dual vector spaces find application in many branches of mathematics that use vector spaces, such as in tensor analysis with finite-dimensional vector spaces. When applied to vector spaces of functions (which are typically infinite-dimensional), dual spaces are used to describe measures, distributions, and Hilbert spaces. Consequently, the dual space is an important concept in functional analysis. Early terms for dual include polarer Raum [Hahn 1927], espace conjugué, adjoint space [Alaoglu 1940], and transponierter Raum [Schauder 1930] and [Banach 1932]. The term dual is due to Bourbaki 1938.

### Freebase

Dual space

In mathematics, any vector space, V, has a corresponding dual vector space consisting of all linear functionals on V. Dual vector spaces for finite-dimensional vector spaces can be used for studying tensors. When applied to vector spaces of functions, dual spaces are employed for defining and studying concepts like measures, distributions, and Hilbert spaces. Consequently, the dual space is an important concept in the study of functional analysis. There are two types of dual spaces: the algebraic dual space, and the continuous dual space. The algebraic dual space is defined for all vector spaces. When defined for a topological vector space there is a subspace of this dual space, corresponding to continuous linear functionals, which constitutes a continuous dual space.

### Numerology

Chaldean Numerology

The numerical value of dual space in Chaldean Numerology is:

**7**Pythagorean Numerology

The numerical value of dual space in Pythagorean Numerology is:

**1**

## Translations for **dual space**

### From our Multilingual Translation Dictionary

- double espaceFrench
- दोहरी जगहHindi
- espaço dualPortuguese
- ڈبل جگہUrdu

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"dual space." *Definitions.net.* STANDS4 LLC, 2023. Web. 24 Mar. 2023. <https://www.definitions.net/definition/dual+space>.

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