definition 5.53 Isomorphism

open in the book · parts/02-mathematical-methods/03-linear-algebra-representations.tex:2402 · p. 125

ground object -- no derivation owed

Rests on

depends_on definition 5.37 Linear transformation ¶
- depends_on definition 4.33 Vector space ¶
  - depends_on definition 4.8 Commutativity; abelian structure ¶
    - depends_on definition 4.4 Internal binary operation; magma ¶
      - depends_on definition 4.3 Algebraic structure ¶
      - depends_on definition 4.2 Binary operation ¶
  - depends_on definition 4.32 Field ¶
    - depends_on definition 4.11 Inverse element ¶
      - depends_on definition 4.9 Neutral element ¶
    - depends_on definition 4.20 Monoid ¶
      - depends_on definition 4.9 Neutral element ¶ ↺
      - depends_on definition 4.18 Semigroup ¶
    - depends_on definition 4.30 Ring ¶
      - depends_on definition 4.8 Commutativity; abelian structure ¶ ↺
      - depends_on definition 4.28 Distributivity ¶
      - depends_on definition 4.21 Group ¶
      - depends_on definition 4.18 Semigroup ¶ ↺
  - depends_on definition 4.31 Module ¶
    - depends_on definition 4.29 Action ¶
      - depends_on definition 4.9 Neutral element ¶ ↺
    - depends_on definition 4.28 Distributivity ¶ ↺
    - depends_on definition 4.21 Group ¶ ↺
    - depends_on definition 4.30 Ring ¶ ↺

Supports

depends_on definition 5.57 Automorphism ¶
depends_on proposition 5.104 Criterion for a direct sum ¶
depends_on proposition 5.54 prop:lin-same-dim-isomorphic ¶
depends_on theorem 5.160 Schur's second lemma ¶
- depends_on lemma 25.39 The low-degree images are forced ¶
  - depends_on example 25.45 Weyl ordering collapses ¶
- depends_on theorem 25.38 Groenewold–van Hove ¶
  - depends_on corollary 25.41 Quantization is not a functor ¶
    - depends_on definition 25.42 Ordering rule ¶
      - depends_on definition 25.44 Weyl and normal ordering ¶
      - depends_on proposition 25.43 The size of the ambiguity ¶
  - depends_on remark 24.57 The half-integer, and the honest status of the construction ¶
  - depends_on remark 24.55 What polarization costs ¶

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`	→	Linear transformation	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:2406
`depends_on`	←	Automorphism	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:2500
`depends_on`	←	Criterion for a direct sum	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:4496
`depends_on`	←	prop:lin-same-dim-isomorphic	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:2412
`depends_on`	←	Schur's second lemma	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:7068