lemma 7.121 Contraction of two Levi-Civita symbols

open in the book · parts/02-mathematical-methods/05-real-analysis.tex:3967 · p. 253

Rests on

depends_on equation 7.134 eq:ana-epsilon-curl ¶
proves proof ch:05-real-analysis@proof-74 ¶

Supports

depends_on proposition 7.122 Product identities of the nabla calculus ¶
depends_on proposition 7.123 Second-order identities of the nabla calculus ¶
- depends_on remark 7.124 The Laplacian of a vector field is a Cartesian notion ¶
- depends_on theorem 7.137 Helmholtz decomposition ¶
  - depends_on remark A.527 The hypotheses, and what happens without them ¶
  - depends_on remark 30.46 Why the plane-wave route, and not the potentials ¶
  - depends_on remark 30.27 Two results this chapter borrows from Part II ¶
  - depends_on remark 10.73 What compact support is doing, and the rate that replaces it ¶
  - depends_on remark 10.74 Where the decomposition is used, and what it costs ¶
- depends_on theorem A.523 Helmholtz decomposition: existence ¶
- depends_on theorem A.525 Helmholtz decomposition: uniqueness ¶
  - depends_on remark A.527 The hypotheses, and what happens without them ¶ ↺

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Edges

type	direction	node	provenance	where
`depends_on`	→	eq:ana-epsilon-curl	declared	parts/02-mathematical-methods/05-real-analysis.tex:3975
`depends_on`	←	Product identities of the nabla calculus	declared	parts/02-mathematical-methods/05-real-analysis.tex:4035
`depends_on`	←	Second-order identities of the nabla calculus	declared	parts/02-mathematical-methods/05-real-analysis.tex:4113
`proves`	←	ch:05-real-analysis@proof-74	declared	parts/02-mathematical-methods/05-real-analysis.tex:3978