definition 12.99 Product and entangled vectors

open in the book · parts/02-mathematical-methods/10-hilbert-spaces.tex:2723 · p. 442

ground object -- no derivation owed

Rests on

depends_on definition 12.94 Tensor product of Hilbert spaces ¶
- depends_on definition 12.2 Hilbert space ¶
  - depends_on definition 5.18 Inner product ¶
    - depends_on definition 4.33 Vector space ¶
      - depends_on definition 4.8 Commutativity; abelian structure ¶
      - depends_on definition 4.32 Field ¶
      - depends_on definition 4.31 Module ¶
  - depends_on definition 6.27 Convergence; Cauchy sequence; completeness ¶
    - depends_on definition 6.24 Metric ¶
      - depends_on definition 3.43 Map ¶
      - depends_on definition 3.38 Ordered pair and Cartesian product ¶
  - depends_on equation 5.44 eq:lin-norm-assoc ¶
- depends_on definition 5.110 Bilinear map ¶
  - depends_on definition 5.37 Linear transformation ¶
    - depends_on definition 4.33 Vector space ¶ ↺
- depends_on definition 5.18 Inner product ¶ ↺

Supports

depends_on example 12.100 Entangled vectors exist ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Tensor product of Hilbert spaces	declared	parts/02-mathematical-methods/10-hilbert-spaces.tex:2728
`depends_on`	←	Entangled vectors exist	declared	parts/02-mathematical-methods/10-hilbert-spaces.tex:2739