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

Rests on

• depends_on equation 5.18 eq:lin-angle-def ¶
• depends_on lemma 5.34 Contraction of two Levi–Civita symbols ¶
  • 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 4.32 Field ¶
        • depends_on definition 4.31 Module ¶
    • depends_on definition 5.27 Orthonormal basis ¶
      • depends_on definition 5.26 Orthogonal basis ¶
        • depends_on definition 5.15 Basis ¶
        • depends_on definition 5.24 Orthogonal vectors ¶
      • depends_on definition 5.25 Unit vector ¶
        • depends_on definition 5.19 Norm ¶
  • proves proof ch:03-linear-algebra-representations@proof-9 ¶
• depends_on lemma 5.33 Determinant through the Levi–Civita symbol ¶
  • depends_on definition 5.32 Levi–Civita symbol; cross product ¶ ↺
  • depends_on equation 5.19 eq:lin-leibniz-det ¶
  • proves proof ch:03-linear-algebra-representations@proof-8 ¶
• proves proof ch:03-linear-algebra-representations@proof-10 ¶

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