Dual space, the Glossary

Table of Contents

1. 115 relations: Absolute value, Algebra over a field, American Mathematical Society, Annihilator (ring theory), Antihomomorphism, Antiisomorphism, Arzelà–Ascoli theorem, Axiom of choice, Banach space, Basis (linear algebra), Bijection, Bilinear form, Bilinear map, Bounded set (topological vector space), Bra–ket notation, Cantor's diagonal argument, Cardinal number, Category theory, Compact operator, Complete topological vector space, Complex conjugate of a vector space, Complex number, Continuous function, Continuous linear operator, Countable set, Covariance and contravariance of vectors, Degenerate bilinear form, Dimension (vector space), Dimensional analysis, Dimensionless quantity, Direct product, Direct sum of modules, Discontinuous linear map, Distribution (mathematics), Dual basis, Dual module, Dual norm, Dual system, Duality (mathematics), Duality (projective geometry), Erdős–Kaplansky theorem, Euclidean space, Euclidean vector, Field (mathematics), Fourier analysis, Frequency, Function composition, Functional (mathematics), Functional analysis, Functor, ... Expand index (65 more) »

2. Linear functionals

Absolute value

In mathematics, the absolute value or modulus of a real number x, is the non-negative value without regard to its sign.

See Dual space and Absolute value

Algebra over a field

In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product.

See Dual space and Algebra over a field

American Mathematical Society

The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.

See Dual space and American Mathematical Society

Annihilator (ring theory)

In mathematics, the annihilator of a subset of a module over a ring is the ideal formed by the elements of the ring that give always zero when multiplied by each element of.

See Dual space and Annihilator (ring theory)

Antihomomorphism

In mathematics, an antihomomorphism is a type of function defined on sets with multiplication that reverses the order of multiplication.

See Dual space and Antihomomorphism

Antiisomorphism

In category theory, a branch of mathematics, an antiisomorphism (or anti-isomorphism) between structured sets A and B is an isomorphism from A to the opposite of B (or equivalently from the opposite of A to B).

See Dual space and Antiisomorphism

Arzelà–Ascoli theorem

The Arzelà–Ascoli theorem is a fundamental result of mathematical analysis giving necessary and sufficient conditions to decide whether every sequence of a given family of real-valued continuous functions defined on a closed and bounded interval has a uniformly convergent subsequence.

See Dual space and Arzelà–Ascoli theorem

Axiom of choice

In mathematics, the axiom of choice, abbreviated AC or AoC, is an axiom of set theory equivalent to the statement that a Cartesian product of a collection of non-empty sets is non-empty.

See Dual space and Axiom of choice

Banach space

In mathematics, more specifically in functional analysis, a Banach space (pronounced) is a complete normed vector space. Dual space and Banach space are functional analysis.

See Dual space and Banach space

Basis (linear algebra)

In mathematics, a set of vectors in a vector space is called a basis (bases) if every element of may be written in a unique way as a finite linear combination of elements of. Dual space and basis (linear algebra) are linear algebra.

See Dual space and Basis (linear algebra)

Bijection

A bijection, bijective function, or one-to-one correspondence between two mathematical sets is a function such that each element of the first set (the domain) is mapped to exactly one element of the second set (the codomain).

See Dual space and Bijection

Bilinear form

In mathematics, a bilinear form is a bilinear map on a vector space (the elements of which are called vectors) over a field K (the elements of which are called scalars). Dual space and bilinear form are linear algebra.

See Dual space and Bilinear form

Bilinear map

In mathematics, a bilinear map is a function combining elements of two vector spaces to yield an element of a third vector space, and is linear in each of its arguments.

See Dual space and Bilinear map

Bounded set (topological vector space)

In functional analysis and related areas of mathematics, a set in a topological vector space is called bounded or von Neumann bounded, if every neighborhood of the zero vector can be inflated to include the set.

See Dual space and Bounded set (topological vector space)

Bra–ket notation

Bra–ket notation, also called Dirac notation, is a notation for linear algebra and linear operators on complex vector spaces together with their dual space both in the finite-dimensional and infinite-dimensional case. Dual space and Bra–ket notation are linear algebra and linear functionals.

See Dual space and Bra–ket notation

Cantor's diagonal argument

Cantor's diagonal argument (among various similar namesthe diagonalisation argument, the diagonal slash argument, the anti-diagonal argument, the diagonal method, and Cantor's diagonalization proof) is a mathematical proof that there are infinite sets which cannot be put into one-to-one correspondence with the infinite set of natural numbersinformally, that there are sets which in some sense contain more elements than there are positive integers.

See Dual space and Cantor's diagonal argument

Cardinal number

In mathematics, a cardinal number, or cardinal for short, is what is commonly called the number of elements of a set.

See Dual space and Cardinal number

Category theory

Category theory is a general theory of mathematical structures and their relations.

See Dual space and Category theory

Compact operator

In functional analysis, a branch of mathematics, a compact operator is a linear operator T: X \to Y, where X,Y are normed vector spaces, with the property that T maps bounded subsets of X to relatively compact subsets of Y (subsets with compact closure in Y).

See Dual space and Compact operator

Complete topological vector space

In functional analysis and related areas of mathematics, a complete topological vector space is a topological vector space (TVS) with the property that whenever points get progressively closer to each other, then there exists some point x towards which they all get closer. Dual space and complete topological vector space are functional analysis.

See Dual space and Complete topological vector space

Complex conjugate of a vector space

In mathematics, the complex conjugate of a complex vector space V\, is a complex vector space \overline V that has the same elements and additive group structure as V, but whose scalar multiplication involves conjugation of the scalars. Dual space and complex conjugate of a vector space are linear algebra.

See Dual space and Complex conjugate of a vector space

Complex number

In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted, called the imaginary unit and satisfying the equation i^.

See Dual space and Complex number

Continuous function

In mathematics, a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function.

See Dual space and Continuous function

Continuous linear operator

In functional analysis and related areas of mathematics, a continuous linear operator or continuous linear mapping is a continuous linear transformation between topological vector spaces. Dual space and continuous linear operator are functional analysis.

See Dual space and Continuous linear operator

Countable set

In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers.

See Dual space and Countable set

Covariance and contravariance of vectors

In physics, especially in multilinear algebra and tensor analysis, covariance and contravariance describe how the quantitative description of certain geometric or physical entities changes with a change of basis.

See Dual space and Covariance and contravariance of vectors

Degenerate bilinear form

In mathematics, specifically linear algebra, a degenerate bilinear form on a vector space V is a bilinear form such that the map from V to V∗ (the dual space of V&hairsp) given by is not an isomorphism. Dual space and degenerate bilinear form are functional analysis.

See Dual space and Degenerate bilinear form

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 over its base field. Dual space and dimension (vector space) are linear algebra.

See Dual space and Dimension (vector space)

Dimensional analysis

In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric current) and units of measurement (such as metres and grams) and tracking these dimensions as calculations or comparisons are performed.

See Dual space and Dimensional analysis

Dimensionless quantity

Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into units of measurement.

See Dual space and Dimensionless quantity

Direct product

In mathematics, one can often define a direct product of objects already known, giving a new one.

See Dual space and Direct product

Direct sum of modules

In abstract algebra, the direct sum is a construction which combines several modules into a new, larger module. Dual space and direct sum of modules are linear algebra.

See Dual space and Direct sum of modules

Discontinuous linear map

In mathematics, linear maps form an important class of "simple" functions which preserve the algebraic structure of linear spaces and are often used as approximations to more general functions (see linear approximation). Dual space and Discontinuous linear map are functional analysis.

See Dual space and Discontinuous linear map

Distribution (mathematics)

Distributions, also known as Schwartz distributions or generalized functions, are objects that generalize the classical notion of functions in mathematical analysis. Dual space and distribution (mathematics) are functional analysis and linear functionals.

See Dual space and Distribution (mathematics)

Dual basis

In linear algebra, given a vector space V with a basis B of vectors indexed by an index set I (the cardinality of I is the dimension of V), the dual set of B is a set B^* of vectors in the dual space V^* with the same index set I such that B and B^* form a biorthogonal system. Dual space and dual basis are linear algebra.

See Dual space and Dual basis

Dual module

In mathematics, the dual module of a left (respectively right) module M over a ring R is the set of left (respectively right) ''R''-module homomorphisms from M to R with the pointwise right (respectively left) module structure.

See Dual space and Dual module

Dual norm

In functional analysis, the dual norm is a measure of size for a continuous linear function defined on a normed vector space. Dual space and dual norm are functional analysis, linear algebra and linear functionals.

See Dual space and Dual norm

Dual system

In mathematics, a dual system, dual pair or a duality over a field \mathbb is a triple (X, Y, b) consisting of two vector spaces, X and Y, over \mathbb and a non-degenerate bilinear map b: X \times Y \to \mathbb. Dual space and dual system are duality theories, functional analysis and linear functionals.

See Dual space and Dual system

Duality (mathematics)

In mathematics, a duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of is, then the dual of is. Dual space and duality (mathematics) are duality theories.

See Dual space and Duality (mathematics)

Duality (projective geometry)

In projective geometry, duality or plane duality is a formalization of the striking symmetry of the roles played by points and lines in the definitions and theorems of projective planes. Dual space and duality (projective geometry) are duality theories.

See Dual space and Duality (projective geometry)

Erdős–Kaplansky theorem

The Erdős–Kaplansky theorem is a theorem from functional analysis. Dual space and Erdős–Kaplansky theorem are functional analysis.

See Dual space and Erdős–Kaplansky theorem

Euclidean space

Euclidean space is the fundamental space of geometry, intended to represent physical space. Dual space and Euclidean space are linear algebra.

See Dual space and Euclidean space

Euclidean vector

In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Dual space and Euclidean vector are linear algebra.

See Dual space and Euclidean vector

Field (mathematics)

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers.

See Dual space and Field (mathematics)

Fourier analysis

In mathematics, Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions.

See Dual space and Fourier analysis

Frequency

Frequency (symbol f), most often measured in hertz (symbol: Hz), is the number of occurrences of a repeating event per unit of time.

See Dual space and Frequency

Function composition

In mathematics, function composition is an operation that takes two functions and, and produces a function such that.

See Dual space and Function composition

Functional (mathematics)

In mathematics, a functional is a certain type of function.

See Dual space and Functional (mathematics)

Functional analysis

Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (for example, inner product, norm, or topology) and the linear functions defined on these spaces and suitably respecting these structures.

See Dual space and Functional analysis

Functor

In mathematics, specifically category theory, a functor is a mapping between categories.

See Dual space and Functor

Galois connection

In mathematics, especially in order theory, a Galois connection is a particular correspondence (typically) between two partially ordered sets (posets).

See Dual space and Galois connection

Generalized function

In mathematics, generalized functions are objects extending the notion of functions on real or complex numbers.

See Dual space and Generalized function

Hahn–Banach theorem

The Hahn–Banach theorem is a central tool in functional analysis. Dual space and Hahn–Banach theorem are linear algebra and linear functionals.

See Dual space and Hahn–Banach theorem

Hausdorff space

In topology and related branches of mathematics, a Hausdorff space, separated space or T2 space is a topological space where, for any two distinct points, there exist neighbourhoods of each that are disjoint from each other.

See Dual space and Hausdorff space

Hölder's inequality

In mathematical analysis, Hölder's inequality, named after Otto Hölder, is a fundamental inequality between integrals and an indispensable tool for the study of ''Lp'' spaces.

See Dual space and Hölder's inequality

Hermitian adjoint

In mathematics, specifically in operator theory, each linear operator A on an inner product space defines a Hermitian adjoint (or adjoint) operator A^* on that space according to the rule where \langle \cdot,\cdot \rangle is the inner product on the vector space.

See Dual space and Hermitian adjoint

Hilbert space

In mathematics, Hilbert spaces (named after David Hilbert) allow the methods of linear algebra and calculus to be generalized from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Dual space and Hilbert space are functional analysis and linear algebra.

See Dual space and Hilbert space

Homomorphism

In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces).

See Dual space and Homomorphism

Identity matrix

In linear algebra, the identity matrix of size n is the n\times n square matrix with ones on the main diagonal and zeros elsewhere.

See Dual space and Identity matrix

Injective function

In mathematics, an injective function (also known as injection, or one-to-one function) is a function that maps distinct elements of its domain to distinct elements; that is, implies.

See Dual space and Injective function

Inverse second

The inverse second or reciprocal second (s−1), also called per second, is a unit defined as the multiplicative inverse of the second (a unit of time).

See Dual space and Inverse second

Isometry

In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective.

See Dual space and Isometry

Isomorphism

In mathematics, an isomorphism is a structure-preserving mapping between two structures of the same type that can be reversed by an inverse mapping.

See Dual space and Isomorphism

Isomorphism theorems

In mathematics, specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship between quotients, homomorphisms, and subobjects.

See Dual space and Isomorphism theorems

Kernel (algebra)

In algebra, the kernel of a homomorphism (function that preserves the structure) is generally the inverse image of 0 (except for groups whose operation is denoted multiplicatively, where the kernel is the inverse image of 1).

See Dual space and Kernel (algebra)

Kronecker delta

In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers.

See Dual space and Kronecker delta

Level set

In mathematics, a level set of a real-valued function of real variables is a set where the function takes on a given constant value, that is: When the number of independent variables is two, a level set is called a level curve, also known as contour line or isoline; so a level curve is the set of all real-valued solutions of an equation in two variables and.

See Dual space and Level set

Limit of a sequence

As the positive integer n becomes larger and larger, the value n\times \sin\left(\tfrac1\right) becomes arbitrarily close to 1.

See Dual space and Limit of a sequence

Linear form

In mathematics, a linear form (also known as a linear functional, a one-form, or a covector) is a linear mapIn some texts the roles are reversed and vectors are defined as linear maps from covectors to scalars from a vector space to its field of scalars (often, the real numbers or the complex numbers). Dual space and linear form are functional analysis, linear algebra and linear functionals.

See Dual space and Linear form

Linear independence

In the theory of vector spaces, a set of vectors is said to be if there exists no nontrivial linear combination of the vectors that equals the zero vector. Dual space and linear independence are linear algebra.

See Dual space and Linear independence

Linear map

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 V \to W between two vector spaces that preserves the operations of vector addition and scalar multiplication.

See Dual space and Linear map

Linear subspace

In mathematics, and more specifically in linear algebra, a linear subspace or vector subspaceThe term linear subspace is sometimes used for referring to flats and affine subspaces. Dual space and linear subspace are functional analysis and linear algebra.

See Dual space and Linear subspace

Locally convex topological vector space

In functional analysis and related areas of mathematics, locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS) that generalize normed spaces. Dual space and locally convex topological vector space are functional analysis.

See Dual space and Locally convex topological vector space

Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

See Dual space and Mathematics

Matrix (mathematics)

In mathematics, a matrix (matrices) is a rectangular array or table of numbers, symbols, or expressions, with elements or entries arranged in rows and columns, which is used to represent a mathematical object or property of such an object.

See Dual space and Matrix (mathematics)

Matrix multiplication

In mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices.

See Dual space and Matrix multiplication

Measure (mathematics)

In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as magnitude, mass, and probability of events.

See Dual space and Measure (mathematics)

Module (mathematics)

In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a ring.

See Dual space and Module (mathematics)

Natural transformation

In category theory, a branch of mathematics, a natural transformation provides a way of transforming one functor into another while respecting the internal structure (i.e., the composition of morphisms) of the categories involved.

See Dual space and Natural transformation

Nicolas Bourbaki

Nicolas Bourbaki is the collective pseudonym of a group of mathematicians, predominantly French alumni of the École normale supérieure (ENS).

See Dual space and Nicolas Bourbaki

Normed vector space

In mathematics, a normed vector space or normed space is a vector space over the real or complex numbers on which a norm is defined.

See Dual space and Normed vector space

One-form (differential geometry)

In differential geometry, a one-form (or covector field) on a differentiable manifold is a differential form of degree one, that is, a smooth section of the cotangent bundle.

See Dual space and One-form (differential geometry)

Orthogonal complement

In the mathematical fields of linear algebra and functional analysis, the orthogonal complement of a subspace W of a vector space V equipped with a bilinear form B is the set W^\perpof all vectors in V that are orthogonal to every vector in W. Informally, it is called the perp, short for perpendicular complement. Dual space and orthogonal complement are functional analysis and linear algebra.

See Dual space and Orthogonal complement

Pointwise

In mathematics, the qualifier pointwise is used to indicate that a certain property is defined by considering each value f(x) of some function f. An important class of pointwise concepts are the pointwise operations, that is, operations defined on functions by applying the operations to function values separately for each point in the domain of definition.

See Dual space and Pointwise

Pontryagin duality

In mathematics, Pontryagin duality is a duality between locally compact abelian groups that allows generalizing Fourier transform to all such groups, which include the circle group (the multiplicative group of complex numbers of modulus one), the finite abelian groups (with the discrete topology), and the additive group of the integers (also with the discrete topology), the real numbers, and every finite-dimensional vector space over the reals or a p-adic field. Dual space and Pontryagin duality are duality theories.

See Dual space and Pontryagin duality

Pullback (differential geometry)

Let \phi:M\to N be a smooth map between smooth manifolds M and N. Then there is an associated linear map from the space of 1-forms on N (the linear space of sections of the cotangent bundle) to the space of 1-forms on M. This linear map is known as the pullback (by \phi), and is frequently denoted by \phi^*.

See Dual space and Pullback (differential geometry)

Quantum mechanics

Quantum mechanics is a fundamental theory that describes the behavior of nature at and below the scale of atoms.

See Dual space and Quantum mechanics

Quotient space (linear algebra)

In linear algebra, the quotient of a vector space V by a subspace N is a vector space obtained by "collapsing" N to zero. Dual space and quotient space (linear algebra) are functional analysis and linear algebra.

See Dual space and Quotient space (linear algebra)

Real number

In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature.

See Dual space and Real number

Reciprocal lattice

In physics, the reciprocal lattice emerges from the Fourier transform of another lattice.

See Dual space and Reciprocal lattice

Reciprocal length

Reciprocal length or inverse length is a quantity or measurement used in several branches of science and mathematics, defined as the reciprocal of length.

See Dual space and Reciprocal length

Reflexive space

In the area of mathematics known as functional analysis, a reflexive space is a locally convex topological vector space for which the canonical evaluation map from X into its bidual (which is the strong dual of the strong dual of X) is a homeomorphism (or equivalently, a TVS isomorphism). Dual space and reflexive space are duality theories.

See Dual space and Reflexive space

Riesz representation theorem

The Riesz representation theorem, sometimes called the Riesz–Fréchet representation theorem after Frigyes Riesz and Maurice René Fréchet, establishes an important connection between a Hilbert space and its continuous dual space. Dual space and Riesz representation theorem are duality theories and linear functionals.

See Dual space and Riesz representation theorem

Riesz–Markov–Kakutani representation theorem

In mathematics, the Riesz–Markov–Kakutani representation theorem relates linear functionals on spaces of continuous functions on a locally compact space to measures in measure theory. Dual space and Riesz–Markov–Kakutani representation theorem are duality theories and linear functionals.

See Dual space and Riesz–Markov–Kakutani representation theorem

Schwartz space

In mathematics, Schwartz space \mathcal is the function space of all functions whose derivatives are rapidly decreasing.

See Dual space and Schwartz space

Second

The second (symbol: s) is the unit of time in the International System of Units (SI), historically defined as of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds each (24 × 60 × 60.

See Dual space and Second

Seminorm

In mathematics, particularly in functional analysis, a seminorm is a norm that need not be positive definite. Dual space and seminorm are linear algebra.

See Dual space and Seminorm

Separable space

In mathematics, a topological space is called separable if it contains a countable, dense subset; that is, there exists a sequence \_^ of elements of the space such that every nonempty open subset of the space contains at least one element of the sequence.

See Dual space and Separable space

Sequence

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

See Dual space and Sequence

Sesquilinear form

In mathematics, a sesquilinear form is a generalization of a bilinear form that, in turn, is a generalization of the concept of the dot product of Euclidean space. Dual space and sesquilinear form are functional analysis and linear algebra.

See Dual space and Sesquilinear form

Spaces of test functions and distributions

In mathematical analysis, the spaces of test functions and distributions are topological vector spaces (TVSs) that are used in the definition and application of distributions. Dual space and spaces of test functions and distributions are functional analysis.

See Dual space and Spaces of test functions and distributions

Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

See Dual space and Springer Science+Business Media

Strong dual space

In functional analysis and related areas of mathematics, the strong dual space of a topological vector space (TVS) X is the continuous dual space X^ of X equipped with the strong (dual) topology or the topology of uniform convergence on bounded subsets of X, where this topology is denoted by b\left(X^, X\right) or \beta\left(X^, X\right). Dual space and strong dual space are functional analysis and linear functionals.

See Dual space and Strong dual space

Strong topology

In mathematics, a strong topology is a topology which is stronger than some other "default" topology.

See Dual space and Strong topology

Surjective function

In mathematics, a surjective function (also known as surjection, or onto function) is a function such that, for every element of the function's codomain, there exists one element in the function's domain such that.

See Dual space and Surjective function

Tensor

In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space.

See Dual space and Tensor

Tensor contraction

In multilinear algebra, a tensor contraction is an operation on a tensor that arises from the canonical pairing of a vector space and its dual.

See Dual space and Tensor contraction

Time–frequency analysis

In signal processing, time–frequency analysis comprises those techniques that study a signal in both the time and frequency domains simultaneously, using various time–frequency representations.

See Dual space and Time–frequency analysis

Topological vector space

In mathematics, a topological vector space (also called a linear topological space and commonly abbreviated TVS or t.v.s.) is one of the basic structures investigated in functional analysis.

See Dual space and Topological vector space

Totally bounded space

In topology and related branches of mathematics, total-boundedness is a generalization of compactness for circumstances in which a set is not necessarily closed. Dual space and Totally bounded space are functional analysis.

See Dual space and Totally bounded space

Transpose

In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix by producing another matrix, often denoted by (among other notations). Dual space and transpose are linear algebra.

See Dual space and Transpose

Uniform norm

In mathematical analysis, the uniform norm assigns to real- or complex-valued bounded functions defined on a set the non-negative number This norm is also called the, the, the, or, when the supremum is in fact the maximum, the. Dual space and uniform norm are functional analysis.

See Dual space and Uniform norm

Unit of time

A unit of time is any particular time interval, used as a standard way of measuring or expressing duration.

See Dual space and Unit of time

Vector space

In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called ''vectors'', can be added together and multiplied ("scaled") by numbers called ''scalars''.

See Dual space and Vector space

Weak topology

In mathematics, weak topology is an alternative term for certain initial topologies, often on topological vector spaces or spaces of linear operators, for instance on a Hilbert space.

See Dual space and Weak topology

See also

Linear functionals

• Banach–Alaoglu theorem
• Bipolar theorem
• Bra–ket notation
• Conjugate index
• Distribution (mathematics)
• Dual norm
• Dual space
• Dual system
• Dual topology
• Friedrichs's inequality
• Fundamental theorem of Hilbert spaces
• Hahn–Banach theorem
• Hyperplane separation theorem
• Linear form
• Mackey–Arens theorem
• Polar set
• Polar topology
• Positive linear functional
• Riesz representation theorem
• Riesz–Markov–Kakutani representation theorem
• Strong dual space
• Transpose of a linear map

References

[1] https://en.wikipedia.org/wiki/Dual_space

Also known as Algebraic dual, Algebraic dual space, Annihilator (linear algebra), Continuous dual, Dual (linear algebra), Dual vector space, Duality (linear algebra), James map, Norm dual, Topological dual space.

, Galois connection, Generalized function, Hahn–Banach theorem, Hausdorff space, Hölder's inequality, Hermitian adjoint, Hilbert space, Homomorphism, Identity matrix, Injective function, Inverse second, Isometry, Isomorphism, Isomorphism theorems, Kernel (algebra), Kronecker delta, Level set, Limit of a sequence, Linear form, Linear independence, Linear map, Linear subspace, Locally convex topological vector space, Mathematics, Matrix (mathematics), Matrix multiplication, Measure (mathematics), Module (mathematics), Natural transformation, Nicolas Bourbaki, Normed vector space, One-form (differential geometry), Orthogonal complement, Pointwise, Pontryagin duality, Pullback (differential geometry), Quantum mechanics, Quotient space (linear algebra), Real number, Reciprocal lattice, Reciprocal length, Reflexive space, Riesz representation theorem, Riesz–Markov–Kakutani representation theorem, Schwartz space, Second, Seminorm, Separable space, Sequence, Sesquilinear form, Spaces of test functions and distributions, Springer Science+Business Media, Strong dual space, Strong topology, Surjective function, Tensor, Tensor contraction, Time–frequency analysis, Topological vector space, Totally bounded space, Transpose, Uniform norm, Unit of time, Vector space, Weak topology.