definition 5.16 Dimension

open in the book · parts/02-mathematical-methods/03-linear-algebra-representations.tex:851 · p. 106

ground object -- no derivation owed

Rests on

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 4.8 Commutativity; abelian structure ¶
      - depends_on definition 4.32 Field ¶
      - depends_on definition 4.31 Module ¶
  - 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 ¶ ↺

Supports

depends_on definition 5.142 Dimension of a representation ¶
depends_on proposition 5.54 prop:lin-same-dim-isomorphic ¶

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`	→	Basis	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:856
`depends_on`	←	Dimension of a representation	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:6216
`depends_on`	←	prop:lin-same-dim-isomorphic	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:2412