proposition 5.114 prop:lin-bilinear-dual

open in the book · parts/02-mathematical-methods/03-linear-algebra-representations.tex:4883 · p. 153

Rests on

depends_on definition 5.110 Bilinear map ¶
- 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 ¶ ↺
depends_on definition 5.59 Dual space ¶
- depends_on definition 5.46 Functional ¶
  - depends_on definition 5.37 Linear transformation ¶ ↺
depends_on definition 5.113 Non-degenerate form ¶
- depends_on definition 5.110 Bilinear map ¶ ↺
depends_on equation 5.87 eq:lin-dual-expansion ¶
depends_on equation 5.86 eq:lin-functional3 ¶
proves proof ch:03-linear-algebra-representations@proof-52 ¶

Nothing declares a dependency on this node yet.

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Bilinear map	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:4899
`depends_on`	→	Dual space	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:4899
`depends_on`	→	Non-degenerate form	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:4899
`depends_on`	→	eq:lin-dual-expansion	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:4899
`depends_on`	→	eq:lin-functional3	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:4899
`proves`	←	ch:03-linear-algebra-representations@proof-52	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:4902