proposition 5.112 Symmetric–antisymmetric splitting

open in the book · parts/02-mathematical-methods/03-linear-algebra-representations.tex:4830 · 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 5.111 Symmetric and antisymmetric forms ¶
- depends_on definition 5.110 Bilinear map ¶ ↺
- depends_on equation 5.137 eq:lin-bilinear-matrix ¶
proves proof ch:03-linear-algebra-representations@proof-51 ¶

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:4841
`depends_on`	→	Symmetric and antisymmetric forms	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:4841
`proves`	←	ch:03-linear-algebra-representations@proof-51	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:4844