proposition 5.61 Annihilator of a subspace

open in the book · parts/02-mathematical-methods/03-linear-algebra-representations.tex:2690 · p. 129

Rests on

depends_on definition 5.59 Dual space ¶
- depends_on definition 5.46 Functional ¶
  - 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 4.32 Field ¶
      - depends_on definition 4.31 Module ¶
depends_on definition 5.7 Vector subspace ¶
- depends_on definition 5.5 Linear combination ¶
  - depends_on definition 4.33 Vector space ¶ ↺
depends_on lemma 5.38 Exchange and completion ¶
- 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 5.7 Vector subspace ¶ ↺
    - 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 5.12 Subspace generated by a set of vectors ¶ ↺
- depends_on definition 5.14 Linear independence ¶ ↺
- proves proof ch:03-linear-algebra-representations@proof-11 ¶
proves proof ch:03-linear-algebra-representations@proof-21 ¶

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Dual space	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:2703
`depends_on`	→	Vector subspace	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:2703
`depends_on`	→	Exchange and completion	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:2703
`depends_on`	←	A functional that annihilates a set of constraints	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:2731
`proves`	←	ch:03-linear-algebra-representations@proof-21	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:2706