Treatise of Physics

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definition 12.94 Tensor product of Hilbert spaces

open in the book · parts/02-mathematical-methods/10-hilbert-spaces.tex:2580 · p. 441

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definition 12.94: Tensor product of Hilbert spaces12.94definition 12.2: Hilbert space12.2definition 5.110: Bilinear map5.110definition 5.18: Inner product5.18definition 12.99: Product and entangled vectors12.99example 12.98: Two particles in three-dimensional space12.98proposition 12.95: The tensor inner product is well defined and positive definite12.95definition 6.27: Convergence; Cauchy sequence; completeness6.27equation 5.44: eq:lin-norm-assoc5.44definition A.278: Countably Hilbert nuclear spaceA.278definition 12.32: Separable Hilbert space12.32definition 10.85: Sobolev space10.85example 12.9: The sequence space \ell^212.9example 12.11: The function space L^212.11lemma A.254: Riemann integral of a continuous curveA.254proposition 12.4: Cauchy–Schwarz and continuity of the inner product12.4proposition 12.28: Convergence criterion for orthogonal series12.28proposition 12.51: The three cases are exclusive and exhaustive12.51theorem 16.70: The direct method16.70theorem 12.14: Closest point in a closed convex set12.14theorem 10.88: Lax–Milgram10.88definition 5.37: Linear transformation5.37definition 5.113: Non-degenerate form5.113definition 5.111: Symmetric and antisymmetric forms5.111lemma 5.137: The alternating top form is unique up to scale5.137proposition 5.114: prop:lin-bilinear-dual5.114proposition 5.112: Symmetric–antisymmetric splitting5.112proposition 5.119: Normal form of a non-degenerate antisymmetric form5.119theorem 5.116: Sylvester's law of inertia5.116definition 4.33: Vector space4.33corollary 5.29: Orthogonal decomposition5.29definition 7.96: Plane7.96definition 5.41: Adjoint5.41definition 5.32: Levi–Civita symbol; cross product5.32definition 5.24: Orthogonal vectors5.24definition 5.144: Unitary representation5.144proposition 12.6: Parallelogram law and polarization12.6proposition 5.63: prop:lin-dual-inner-product5.63proposition 5.31: Gram criterion5.31proposition 5.28: Gram–Schmidt5.28neighborhood truncated

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typedirectionnode provenancewhere
depends_on → Hilbert space declared parts/02-mathematical-methods/10-hilbert-spaces.tex:2596
depends_on → Bilinear map declared parts/02-mathematical-methods/10-hilbert-spaces.tex:2596
depends_on → Inner product declared parts/02-mathematical-methods/10-hilbert-spaces.tex:2596
depends_on ← Product and entangled vectors declared parts/02-mathematical-methods/10-hilbert-spaces.tex:2728
depends_on ← Two particles in three-dimensional space declared parts/02-mathematical-methods/10-hilbert-spaces.tex:2720
depends_on ← The tensor inner product is well defined and positive definite declared parts/02-mathematical-methods/10-hilbert-spaces.tex:2608