definition 5.145 Equivalent representations

open in the book · parts/02-mathematical-methods/03-linear-algebra-representations.tex:6278 · p. 170

ground object -- no derivation owed

Rests on

depends_on definition 5.141 Representation of a group ¶
- depends_on definition 4.21 Group ¶
  - depends_on definition 4.11 Inverse element ¶
    - depends_on definition 4.9 Neutral element ¶
      - depends_on definition 4.3 Algebraic structure ¶
  - depends_on definition 4.20 Monoid ¶
    - depends_on definition 4.9 Neutral element ¶ ↺
    - depends_on definition 4.18 Semigroup ¶
      - depends_on definition 4.6 Associativity ¶
      - depends_on definition 4.4 Internal binary operation; magma ¶
- depends_on definition 4.43 Group homomorphism ¶
  - depends_on definition 4.21 Group ¶ ↺
  - depends_on definition 3.43 Map ¶
    - depends_on definition 3.24 Quantifiers ¶
      - depends_on definition 3.23 Predicate ¶
    - depends_on definition 3.28 Set ¶
- depends_on definition 4.48 Symmetric group ¶
  - depends_on definition 3.47 Bijective map ¶

Supports

depends_on proposition 5.155 Averaging trick ¶
- depends_on theorem 101.62 The mixing matrix is unitary ¶
  - depends_on proposition 101.63 Parameter counting, and why three generations permit $CP$ violation ¶
  - depends_on theorem 103.11 GIM suppression at one loop ¶
    - depends_on phenomenon 103.42 $CP$ violation in charm decays ¶
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`	→	Representation of a group	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:6287
`depends_on`	←	Averaging trick	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:6603
`depends_on`	←	Schur's second lemma	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:7068