definition 5.59 Dual space

open in the book · parts/02-mathematical-methods/03-linear-algebra-representations.tex:2580 · p. 127

ground object -- no derivation owed

Rests on

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 4.4 Internal binary operation; magma ¶
    - depends_on definition 4.32 Field ¶
      - depends_on definition 4.11 Inverse element ¶
      - depends_on definition 4.20 Monoid ¶
      - depends_on definition 4.30 Ring ¶
    - depends_on definition 4.31 Module ¶
      - depends_on definition 4.29 Action ¶
      - depends_on definition 4.28 Distributivity ¶
      - depends_on definition 4.21 Group ¶
      - depends_on definition 4.30 Ring ¶ ↺

Supports

depends_on definition 5.66 Pushforward ¶
- depends_on proposition 5.67 Adjointness of pullback and pushforward ¶
depends_on proposition 5.61 Annihilator of a subspace ¶
- depends_on corollary 5.62 A functional that annihilates a set of constraints ¶
depends_on proposition 5.114 prop:lin-bilinear-dual ¶
depends_on proposition 5.63 prop:lin-dual-inner-product ¶
depends_on proposition 5.67 Adjointness of pullback and pushforward ¶ ↺

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`	→	Functional	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:2589
`depends_on`	←	Pushforward	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:2979
`depends_on`	←	Annihilator of a subspace	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:2703
`depends_on`	←	prop:lin-bilinear-dual	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:4899
`depends_on`	←	prop:lin-dual-inner-product	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:2794
`depends_on`	←	Adjointness of pullback and pushforward	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:3009