Revision #530 → #1172 · back to history
addedDual space4a4f343aed17
addedContinuous dual space (intro)33f0b69422c1
addedAlgebraic dual space8f0f4355ddc9
addedA linear functional on R^281895c411ce7
addedCovectors / one-forms / linear forms32ee9fbc6c06
addedNatural pairingee828ccb727b
addedDual setd65020828e65
addedDual set is a basis when finite-dimensional7e436a4b1c14
addedDual basis (finite-dimensional)41735d4ff9d0
addedBi-orthogonality property932adb08a507
addedVerifying a dual basis36dbb0166517
addedDual basis of a non-orthogonal basis of R^26516474f1215
addedMatrix biorthogonality of basis and dual basisfc077aacb3f1
addedLevel curves of a functional as parallel lines6e7226574ba6
addedInfinite-dimensional dual: independent but not a basis671a4272d3ee
addedDual of finitely-supported real sequencesaf17054ac9af
addedDual identified with function space on a basis25edd2ff9b0b
addedDual of infinite-dimensional space has larger dimension354ee36ab5aa
addedErdős–Kaplansky theoreme7ae04001119
addedV isomorphic to V* but not naturally70ff018e7fc9
addedNondegenerate bilinear form induces isomorphism into dual69a6ff21bef6
addedCorrespondence: isomorphisms into dual vs nondegenerate bilinear forms447014e465e3
addedSesquilinear form gives isomorphism with conjugate dual9c2e119d3b17
addedNatural map into the double dual5c3e9f5da77e
addedDouble-dual map injective, iso iff finite-dimensional09c7e9c72ce3
addedTranspose of a linear map239ed389a53a
addedIdentity characterizing the transpose5386a7d60e33
addedTranspose assignment: injective, iso iff finite-dim, contravariant functora8b7765288c8
addedTranspose represented by transpose matrixd2eed873afc1
addedAnnihilator of a subsetc79382dd18be
addedBasic annihilator properties0869f6a8436c
addedAnnihilators of subsets, sums and intersectionsee181e1a2559
addedDouble annihilator and Galois connection (finite-dim)0454ae75fbe7
addedDual of quotient isomorphic to annihilatord1ddc0e9a769
addedDual of a direct sum2877dc1c1d07
addedDual space as negative-dimensional107e2bd10d83
addedDual space has inverse units (Fourier/physics)8161f6930913
addedContinuous and algebraic dual coincide in finite dimensionse67ad01b028c
addedContinuous dual space134d9935446c
addedTest function spaces and distributions8232c8b852a0
addedDual of a TVS equals dual of its completion7c648b781875
addedPolar topology on the continuous dualdd2526394bcb
addedConvergence of a net of functionals94ea12fffd61
addedConditions on the class of bounded subsetsde34c4469bee
addedResulting topology is Hausdorff with given local base941bf709b38a
addedStrong topology2505a05f94e5
addedStrong topology is normed for normed spaces798a0dc021a7
addedStereotype topology650770c3daf8
addedWeak topology6ee517a81ac9
addedReflexivity variants from the three topologiesb304ba737eb5
addedDual of ℓ^p is ℓ^q4fa5b34b7d6d
addedDuals of ℓ^1, c and c_053423103cd11
addedRiesz representation theorem (Hilbert dual)be11e9c9c8cb
addedRiesz–Markov–Kakutani representation theoremd23f1fb7db1c
addedTranspose of a continuous linear map71a187992c68
addedNorm of transpose equals norm of mapc4e869bc8ba1
addedDense range iff transpose injective3eed89fcba6e
addedTranspose of a compact map is compactd38ad7787f13
addedTranspose and adjoint on a Hilbert space10e5b898ec0a
addedContinuity of the transpose for compatible topologies9054fcf64c8f
addedDuals of quotient and subspace via annihilator560496a1e028
addedSeparable dual implies separable space9b5135049483
addedMap into the continuous double duala5c4e23fa726
addedDouble-dual map is an isometry0f5db671429e
addedReflexive normed space32576039b320
addedDouble-dual map injective for Hausdorff locally convex TVSeab2e78ebf11