lemma 5.34 Contraction of two Levi–Civita symbols

open in the book · parts/02-mathematical-methods/03-linear-algebra-representations.tex:1541 · p. 115

Rests on

depends_on definition 5.32 Levi–Civita symbol; cross product ¶
- depends_on definition 4.48 Symmetric group ¶
  - depends_on definition 3.47 Bijective map ¶
- depends_on definition 5.18 Inner product ¶
  - 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 5.27 Orthonormal basis ¶
  - depends_on definition 5.26 Orthogonal basis ¶
    - depends_on definition 5.15 Basis ¶
      - depends_on definition 5.12 Subspace generated by a set of vectors ¶
      - depends_on definition 5.14 Linear independence ¶
    - depends_on definition 5.24 Orthogonal vectors ¶
      - depends_on definition 5.18 Inner product ¶ ↺
  - depends_on definition 5.25 Unit vector ¶
    - depends_on definition 5.19 Norm ¶
      - depends_on definition 4.33 Vector space ¶ ↺
proves proof ch:03-linear-algebra-representations@proof-9 ¶

Supports

depends_on proposition 5.35 The identities of the vector algebra of $\R^{3}$ ¶

Neighborhood

Every logical edge within two steps of this node.

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Edges

type	direction	node	provenance	where
`depends_on`	→	Levi–Civita symbol; cross product	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:1548
`depends_on`	←	The identities of the vector algebra of $\R^{3}$	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:1613
`proves`	←	ch:03-linear-algebra-representations@proof-9	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:1551