• Study Resource
  • Explore
    • Arts & Humanities
    • Business
    • Engineering & Technology
    • Foreign Language
    • History
    • Math
    • Science
    • Social Science

    Top subcategories

    • Advanced Math
    • Algebra
    • Basic Math
    • Calculus
    • Geometry
    • Linear Algebra
    • Pre-Algebra
    • Pre-Calculus
    • Statistics And Probability
    • Trigonometry
    • other →

    Top subcategories

    • Astronomy
    • Astrophysics
    • Biology
    • Chemistry
    • Earth Science
    • Environmental Science
    • Health Science
    • Physics
    • other →

    Top subcategories

    • Anthropology
    • Law
    • Political Science
    • Psychology
    • Sociology
    • other →

    Top subcategories

    • Accounting
    • Economics
    • Finance
    • Management
    • other →

    Top subcategories

    • Aerospace Engineering
    • Bioengineering
    • Chemical Engineering
    • Civil Engineering
    • Computer Science
    • Electrical Engineering
    • Industrial Engineering
    • Mechanical Engineering
    • Web Design
    • other →

    Top subcategories

    • Architecture
    • Communications
    • English
    • Gender Studies
    • Music
    • Performing Arts
    • Philosophy
    • Religious Studies
    • Writing
    • other →

    Top subcategories

    • Ancient History
    • European History
    • US History
    • World History
    • other →

    Top subcategories

    • Croatian
    • Czech
    • Finnish
    • Greek
    • Hindi
    • Japanese
    • Korean
    • Persian
    • Swedish
    • Turkish
    • other →
 
Profile Documents Logout
Upload
Slides
Slides

Completely ultrametrizable spaces and continuous
Completely ultrametrizable spaces and continuous

Banach precompact elements of a locally m-convex Bo
Banach precompact elements of a locally m-convex Bo

FUNDAMENTAL GROUPS AND THE VAN KAMPEN`S THEOREM
FUNDAMENTAL GROUPS AND THE VAN KAMPEN`S THEOREM

WHAT IS A POLYNOMIAL? 1. A Construction of the Complex
WHAT IS A POLYNOMIAL? 1. A Construction of the Complex

Computing in Picard groups of projective curves over finite fields
Computing in Picard groups of projective curves over finite fields

Locally compact quantum groups 1. Locally compact groups from an
Locally compact quantum groups 1. Locally compact groups from an

... Let G be a locally compact group, and consider C0 (G ), C b (G ) and L∞ (G ) (left Haar measure). These are two C∗ -algebras and a von Neumann algebra: they depend only on the topological and measure space properties of G . For example, in the case when G is countable and discrete, these algebras ca ...
MATH10212 Linear Algebra Systems of Linear Equations
MATH10212 Linear Algebra Systems of Linear Equations

Characteristic polynomials of unitary matrices
Characteristic polynomials of unitary matrices

filter convergence structures on posets
filter convergence structures on posets

We consider the projection : SO(3) ! S 2, where we send a matrix to
We consider the projection : SO(3) ! S 2, where we send a matrix to

Modules I: Basic definitions and constructions
Modules I: Basic definitions and constructions

Rings of functions in Lipschitz topology
Rings of functions in Lipschitz topology

... Let X atd,Ibe metric spaces with metrics d and d', respectively. A map f: X-Y is Lipschitz if there is I>0 such that d'(f(*),-f(y))=Ld(x,y) for all x,yCX. The smallest such I is the Lipschitz constant lip f of f. These notions make sense also for pseudometric spaces. If each point of X has a neighbo ...
7 Symplectic Quotients
7 Symplectic Quotients

A NEW PROOF OF E. CARTAN`S THEOREM ON
A NEW PROOF OF E. CARTAN`S THEOREM ON

(January 14, 2009) [16.1] Let p be the smallest prime dividing the
(January 14, 2009) [16.1] Let p be the smallest prime dividing the

De Rham cohomology of algebraic varieties
De Rham cohomology of algebraic varieties

Constructible, open, and closed sets
Constructible, open, and closed sets

Homework assignments
Homework assignments

19 Orthogonal projections and orthogonal matrices
19 Orthogonal projections and orthogonal matrices

GLn(R) AS A LIE GROUP Contents 1. Matrix Groups over R, C, and
GLn(R) AS A LIE GROUP Contents 1. Matrix Groups over R, C, and

arXiv:1705.08225v1 [math.NT] 23 May 2017
arXiv:1705.08225v1 [math.NT] 23 May 2017

Existence and uniqueness of Haar integrals
Existence and uniqueness of Haar integrals

Splitting of short exact sequences for modules
Splitting of short exact sequences for modules

Regression Analysis
Regression Analysis

< 1 ... 29 30 31 32 33 34 35 36 37 ... 74 >

Dual space

In mathematics, any vector space V has a corresponding dual vector space (or just dual space for short) consisting of all linear functionals on V together with a naturally induced linear structure. Dual vector spaces for finite-dimensional vector spaces show up in tensor analysis. 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.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.
  • studyres.com © 2025
  • DMCA
  • Privacy
  • Terms
  • Report