proposition 5.161 Irreducible representations of an abelian group

open in the book · parts/02-mathematical-methods/03-linear-algebra-representations.tex:7120 · p. 181

Rests on

depends_on definition 5.148 Irreducible representation ¶
- depends_on definition 5.147 Invariant subspace ¶
  - depends_on definition 5.7 Vector subspace ¶
    - depends_on definition 5.5 Linear combination ¶
      - depends_on definition 4.33 Vector space ¶
  - 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 4.20 Monoid ¶
    - depends_on definition 4.43 Group homomorphism ¶
      - depends_on definition 4.21 Group ¶ ↺
      - depends_on definition 3.43 Map ¶
    - depends_on definition 4.48 Symmetric group ¶
      - depends_on definition 3.47 Bijective map ¶
depends_on theorem 5.158 Schur's first lemma ¶
- depends_on definition 5.37 Linear transformation ¶
  - depends_on definition 4.33 Vector space ¶ ↺
- depends_on definition 5.147 Invariant subspace ¶ ↺
- depends_on definition 5.148 Irreducible representation ¶ ↺
- proves proof ch:03-linear-algebra-representations@proof-67 ¶
proves proof ch:03-linear-algebra-representations@proof-69 ¶

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type	direction	node	provenance	where
`depends_on`	→	Irreducible representation	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:7127
`depends_on`	→	Schur's first lemma	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:7127
`proves`	←	ch:03-linear-algebra-representations@proof-69	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:7130