lemma A.90 Affine normalization

open in the book · appendices/A-long-proofs.tex:5576 · p. 2838

Rests on

depends_on proposition A.89 Beltrami form ¶
- depends_on equation A.218 eq:app-korn-lichtenstein-wirtinger ¶
- depends_on proposition A.87 The isothermal system ¶
  - depends_on equation 10.11 eq:pde-two-variable-matrix ¶
  - depends_on proposition A.86 The complex characteristic equation ¶
    - depends_on equation 10.8 eq:pde-characteristic-condition ¶
    - depends_on equation 10.12 eq:pde-two-variable-coefficients ¶
    - proves proof app:A-long-proofs@proof-58 ¶
  - proves proof app:A-long-proofs@proof-59 ¶
- proves proof app:A-long-proofs@proof-60 ¶
depends_on theorem 10.8 The type is a coordinate invariant ¶
- depends_on definition 10.6 Type of a second-order operator ¶
  - depends_on definition 10.4 The second-order operator ¶
    - depends_on definition 10.3 Principal part and principal symbol ¶
      - depends_on definition 10.2 Linear, semilinear, quasilinear ¶
      - depends_on equation 10.2 eq:pde-multi-index ¶
    - depends_on proposition 7.105 Clairaut–Schwarz ¶
      - depends_on definition 7.20 Continuity at a point ¶
      - depends_on theorem 7.35 Mean value theorem ¶
      - proves proof ch:05-real-analysis@proof-64 ¶
  - depends_on theorem 5.116 Sylvester's law of inertia ¶
    - depends_on definition 5.110 Bilinear map ¶
      - depends_on definition 5.37 Linear transformation ¶
    - 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 ¶
    - depends_on equation 5.139 eq:lin-bilinear-congruence ¶
    - proves proof ch:03-linear-algebra-representations@proof-53 ¶
- depends_on proposition 7.31 Chain rule ¶
  - depends_on definition 7.13 Composite function ¶
    - depends_on definition 7.9 Real function ¶
      - depends_on definition 3.43 Map ¶
  - depends_on proposition 7.27 Differentiable implies continuous ¶
    - depends_on definition 7.20 Continuity at a point ¶ ↺
    - depends_on definition 7.26 Derivative of a function at a point ¶
      - depends_on definition 7.16 Limit ¶
      - depends_on definition 7.9 Real function ¶ ↺
    - depends_on proposition 7.6 Algebra of limits ¶
      - depends_on definition 7.4 Convergence ¶
      - depends_on proposition 7.3 Triangle inequality ¶
      - proves proof ch:05-real-analysis@proof-3 ¶
    - proves proof ch:05-real-analysis@proof-11 ¶
  - depends_on proposition 7.6 Algebra of limits ¶ ↺
  - proves proof ch:05-real-analysis@proof-15 ¶
- depends_on theorem 5.116 Sylvester's law of inertia ¶ ↺
- proves proof ch:08-pdes@proof-1 ¶
proves proof app:A-long-proofs@proof-61 ¶

Supports

depends_on lemma A.91 Smallness after rescaling ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Beltrami form	declared	appendices/A-long-proofs.tex:5582
`depends_on`	→	The type is a coordinate invariant	declared	appendices/A-long-proofs.tex:5582
`depends_on`	←	Smallness after rescaling	declared	appendices/A-long-proofs.tex:5631
`proves`	←	app:A-long-proofs@proof-61	declared	appendices/A-long-proofs.tex:5585