Revision #572 → #1316 · back to history
addedInner product spaceacb7b62d4e31
addedHilbert space (as complete inner product space)c88e0796af83
addedInner product (formal definition)bc023826a679
addedConjugate symmetry63750e943577
addedLinearity in the first argumentd702b8dca880
addedPositive-definitenesse0c175b71cf4
addedPositive semi-definite Hermitian form is an inner product iff2be98b0cef98
addedInner product is sesquilinear (conjugate-linearity in 2nd argument)8f671ea2f1a3
addedReal inner product is positive-definite symmetric bilinear formd5e9cc9db67b
addedReal numbers as inner product space43975cf690aa
addedComplex numbers as inner product space1a208982d0ca
addedEuclidean vector space with dot product6b3b93f79054
addedCharacterization of inner products on R^n via symmetric positive-definite matrices73adaf525a72
addedHermitian form on complex coordinate space09f5d99e095c
addedSpace of continuous functions with L^2 inner product (incomplete)f571f75eb4d4
addedExpectation as inner product on random variables19671067743c
addedFrobenius inner product on complex matrices68ad2b6420ec
addedCanonical norm induced by inner productb6e1a7ef2eaf
addedCauchy–Schwarz inequality47439786e230
addedParallelogram law characterizes inner-product normsf150dd8948b7
addedPolarization identity22ef1e38e4e1
addedPtolemy's inequality characterizes inner-product normscfb4a93d9dcc
addedOrthogonal vectors242e9aed2e87
addedOperator vanishing characterization via inner product (complex case)8ab330671eab
addedOrthogonal complement11207e84c7a2
addedPythagorean theorem910c965206fb
addedPythagorean theorem for pairwise orthogonal vectorscda03e9ff86c
addedAngle between vectors via Cauchy–Schwarzb4b223ee992d
addedReal part of inner product via polarization identity7a7cc424f57f
addedPolarization identity for complex inner productsf24f28c21565
addedComplex inner product determined by its real part13977df57fb8
addedComplex inner product induced by dot product on C^n50a13816281e
addedReal part of complex inner product is real inner productdf4743f7d87b
added90° rotation counterexample on real inner product space3248be25d1e2
addedOrthonormal basis (finite-dimensional)2afc6b652e2f
addedOrthonormal basis (infinite-dimensional)8366cf7a6574
addedSeparable inner product space has orthonormal basis017161e799ee
addedComplete inner product space has orthonormal basis351e8a8d4817
addedParseval isometry for separable inner product spaces5c537efc485a
addedFourier series orthonormal basis on L^2d021353195fc
addedContinuous linear maps between inner product spaces7a3fc2241aec
addedSymmetric linear operator95daf58affec
addedIsometry between inner product spaces8633365ab0d2
addedMazur–Ulam theorem for isometriesd158a39e7443
addedIsometrical isomorphism / unitary operatore92914006f9d
addedSpectral theorem83e3563325cb
addedDegenerate inner product / semi-norm quotient constructiona6cadf06359d
addedNondegenerate conjugate symmetric formfd777bf45f81
addedSylvester's law of inertia9fde22c74b28
addedMinkowski space as indefinite inner product8d760907efe7