definition 5.142 Dimension of a representation

open in the book · parts/02-mathematical-methods/03-linear-algebra-representations.tex:6213 · p. 169

ground object -- no derivation owed

Rests on

depends_on definition 5.16 Dimension ¶
- depends_on definition 5.15 Basis ¶
  - depends_on definition 5.12 Subspace generated by a set of vectors ¶
    - depends_on definition 5.5 Linear combination ¶
      - depends_on definition 4.33 Vector space ¶
    - depends_on definition 5.7 Vector subspace ¶
      - depends_on definition 5.5 Linear combination ¶ ↺
    - proves proof ch:03-linear-algebra-representations@proof-3 ¶
  - depends_on definition 5.14 Linear independence ¶
    - depends_on definition 5.5 Linear combination ¶ ↺
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 ¶

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type	direction	node	provenance	where
`depends_on`	→	Dimension	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:6216
`depends_on`	→	Representation of a group	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:6216