blanketglossary

Dual space

Definition

In mathematics, any vector space has a corresponding dual vector space consisting of all linear forms on together with the vector space structure of pointwise addition and scalar multiplication by constants.

Related concepts

(0,1)-matrixAbsolute valueAdjoint of an operatorAdjugate matrixAffine coordinate systemAffine geometryAffine groupAffine spaceAffine transformationAlgebra (Lang)Algebra over a fieldAmerican Mathematical SocietyAn Introduction to ManifoldsAnnihilator (ring theory)Antihermitian matrixAntihomomorphismAntiisomorphicApproximation propertyArzelà–Ascoli theoremAxiom of choiceBalanced setBanach algebraBanach spaceBanach–Alaoglu theoremBanach–Mazur distanceBarrelled spaceBasic Linear Algebra SubprogramsBasis (linear algebra)Basis transformation matrixBesov spaceBijectionBilinear formBilinear mappingBiorthogonal systemBivectorBlock matrixBounded operatorBounded set (topological vector space)Bra–ket notationC*-algebraCalculus of variationsCantor's diagonal argumentCardinal numberCardinal numbersCartesian coordinate systemCategory of vector spacesCategory theoryCauchy–Binet formulaCayley–Hamilton theoremChange of basisCharacteristic polynomialCharles W. MisnerCholesky decompositionChoquet theoryCirculant matrixClassical treatment of tensorsClifford algebraClosed graph theorem (functional analysis)Compact operatorComparison of linear algebra librariesComplete topological vector spaceComplex conjugate vector spaceComplex numbersComponent-free treatment of tensorsComposition of mapsContinuous function (topology)Continuous linear functionalContravariant functorCountably infiniteCovariance and contravariance of vectorsCramer's ruleCyclic subspaceDeterminantDiagonal matrixDimension (vector space)Dimension theorem for vector spacesDimensional analysisDimensionlessDirect productDirect sum of modulesDiscontinuous linear mapDistribution (mathematics)Dot productDual basisDual moduleDual normDual pairDual systemDual topologyDuality (mathematics)Duality (projective geometry)Eigenvalue, eigenvector and eigenspaceElementary row operationsErdős–Kaplansky theoremEric W. WeissteinEuclidean groupEuclidean spaceExamples of vector spacesExterior algebraField (mathematics)Finite-dimensionalFirst isomorphism theoremFlat (geometry)Floating-point arithmeticFourier analysisFractionFrançois TrèvesFrequencyFréchet spaceFunctional (mathematics)Functional analysisFunctional calculusGalilean groupGalois connectionGamas's theoremGarrett BirkhoffGaussian eliminationGauss–Jordan eliminationGelfand–Naimark theoremGeneralized functionGeometric algebraGlossary of functional analysisGlossary of linear algebraGraduate Texts in MathematicsGram–Schmidt processGroup algebra of a locally compact groupHahn–Banach theoremHamel basisHamel dimensionHankel matrixHardy spaceHausdorff spaceHaynsworth inertia additivity formulaHeat kernelHelmut H. SchaeferHermitian adjointHermitian matrixHessenberg matrixHessian matrixHigher-order singular value decompositionHilbert spaceHilbert–Schmidt operatorHomomorphismHouseholder transformationHölder's inequalityIdentity matrixIf and only ifImproper rotationIndefinite orthogonal groupIndex theoremInjectiveInner product spaceIntegral linear operatorInvariant subspace problemInverse lengthInverse secondIsometryIsomorphicIsomorphismJohn Archibald WheelerJones polynomialJordan normal formKakutani fixed-point theoremKernel (algebra)Kip S. ThorneKrein–Milman theoremKronecker deltaLU decompositionLeast squaresLevel setLevel setsLimit of a sequenceLinear algebraLinear combinationLinear equationLinear formLinear functionalLinear independenceLinear least squaresLinear mapLinear operatorLinear spanLinear subspaceLinearly independentList of functional analysis topicsList of matricesLocally convex topological vector spaceLoring W. TuLp spaceMackey topologyMackey–Arens theoremMahler's conjectureMathWorldMathematicsMatrix (mathematics)Matrix additionMatrix congruenceMatrix consimilarityMatrix decompositionMatrix equivalenceMatrix inversionMatrix multiplicationMatrix similarityMcGraw-Hill Science/Engineering/MathMeasure (mathematics)Min-max theoremMinor (linear algebra)Module (mathematics)Moore–Penrose pseudoinverseMultilinear algebraMultivectorNatural isomorphismNatural pairingNatural transformationNicolas BourbakiNoncommutative geometryNondegenerate formNorm topologyNormal operatorNormed spaceNormed vector spaceNuclear operatorNuclear spaceNull spaceNull vectorNullity theoremNumerical linear algebraNumerical stabilityOne-formOperator algebraOperator topologiesOrdered pairOrientation (geometry)Orthogonal complementOrthogonal groupOrthogonal matrixOrthogonal projectionOrthogonalityOuter productOutline of linear algebraOvercompletenessPaul HalmosPerron–Frobenius theoremPfaffianPoincaré groupPointwisePolar decompositionPolar setPolar topologyPontryagin dualityPositive-definite matrixProjection (linear algebra)Projective geometryProjective linear groupProjective spaceProjective transformationPseudo-Euclidean spacePullback (differential geometry)QR decompositionQuadricQuantum mechanicsQuotient space (linear algebra)Rank (linear algebra)Rank–nullity theoremReal numberReciprocal latticeReducing subspaceReflexive spaceRiemann hypothesisRiesz representation theoremRiesz–Markov–Kakutani representation theoremRow and column spacesRow equivalenceSaturated familySaunders Mac LaneScalar multiplicationSchur complementSchur decompositionSchwartz spaceSecondSeminormSeparable spaceSequenceSerge LangSesquilinear formShear mappingSheldon AxlerSingular value decompositionSkew-symmetric matrixSobolev spaceSpaces of test functions and distributionsSparse matrixSpectral theoremSpectral theory of ordinary differential equationsSpectrum of a C*-algebraSpectrum of a matrixSpringer Science+Business MediaSqueeze mappingStereotype spaceStochastic matrixStrassen algorithmStrong dual spaceStrong operator topologyStrong topologyStrong topology (polar topology)Supremum normSurjectionSymmetric algebraSymmetric matrixSymplectic structureSystem of linear equationsTensorTensor algebraTensor contractionTerence TaoTime–frequency analysisToeplitz matrixTomita–Takesaki theoryTopological quantum field theoryTopological vector spaceTopologies on spaces of linear mapsTotal setTotally bounded spaceTrace (linear algebra)Trace classTransposeTranspose of a linear mapTriangular matrixTridiagonal matrixUltrastrong topologyUltraweak topologyUnbounded operatorUniform boundedness principleUniform convergenceUnit of timeUnitary matrixUnitary operatorVandermonde matrixVector (geometric)Vector spaceVector subspaceVon Neumann algebraWalter RudinWeak convergence (Hilbert space)Weak operator topologyWeak topologyWeak topology (polar topology)Weyr canonical formWoodbury matrix identityYitzhak Katznelson

28 concepts already in your glossary