remark 22.21 The count

open in the book · parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:702 · p. 813

remark -- no derivation owed by its kind

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depends_on proposition 22.17 Transformation conditions ¶
- depends_on definition 22.15 Canonical transformation ¶
  - depends_on definition 22.14 Phase-space coordinate transformation ¶
    - depends_on definition 22.2 Hamiltonian ¶
      - depends_on definition 21.34 Generalized momentum ¶
      - depends_on definition 21.31 Lagrangian ¶
  - depends_on definition 21.45 Action ¶
    - depends_on definition 16.96 Action; Hamilton's principle ¶
      - depends_on definition 21.31 Lagrangian ¶ ↺
      - depends_on equation 16.11 eq:calcvar-basic-functional ¶
    - depends_on equation 21.37 eq:lag-lagrangian ¶
  - depends_on theorem 22.6 Hamilton's equations ¶
    - depends_on definition 22.2 Hamiltonian ¶ ↺
    - depends_on equation 21.39 eq:lag-el-conservative ¶
    - depends_on equation 21.43 eq:lag-generalized-momentum ¶
    - proves proof ch:05-hamiltonian-mechanics@proof-2 ¶
- depends_on equation 22.14 eq:ham-ct-P ¶
- depends_on equation 22.13 eq:ham-ct-Q ¶
- proves proof ch:05-hamiltonian-mechanics@proof-8 ¶
depends_on proposition 5.139 Dimension of the symplectic group ¶
- depends_on definition 5.127 Lie algebra ¶
  - depends_on definition 5.121 Algebra ¶
    - depends_on definition 4.4 Internal binary operation; magma ¶
      - depends_on definition 4.3 Algebraic structure ¶
      - depends_on definition 4.2 Binary operation ¶
    - 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 5.135 The symplectic group ¶
  - depends_on definition 5.113 Non-degenerate form ¶
    - depends_on definition 5.110 Bilinear map ¶
      - depends_on definition 5.37 Linear transformation ¶
  - depends_on equation 5.138 eq:lin-bilinear-expansion ¶
  - depends_on proposition 5.119 Normal form of a non-degenerate antisymmetric form ¶
    - depends_on definition 5.110 Bilinear map ¶ ↺
    - depends_on definition 5.113 Non-degenerate form ¶ ↺
    - 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-54 ¶
- depends_on proposition 5.125 prop:lin-matrix-algebra ¶
  - depends_on definition 5.121 Algebra ¶ ↺
  - depends_on definition 5.37 Linear transformation ¶ ↺
  - depends_on equation 5.150 eq:lin-ctesesc2 ¶
  - depends_on equation 5.74 eq:lin-matrix-rep ¶
  - depends_on proposition 5.45 prop:lin-matrix-unique ¶
    - 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 5.37 Linear transformation ¶ ↺
    - depends_on equation 5.29 eq:lin-indepli2 ¶
    - depends_on equation 5.74 eq:lin-matrix-rep ¶ ↺
    - proves proof ch:03-linear-algebra-representations@proof-16 ¶
  - proves proof ch:03-linear-algebra-representations@proof-55 ¶
- proves proof ch:03-linear-algebra-representations@proof-62 ¶

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type	direction	node	provenance	where
`depends_on`	→	Transformation conditions	declared	parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:711
`depends_on`	→	Dimension of the symplectic group	declared	parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:711