definition 22.40 Symplectic matrix

open in the book · parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:1336 · p. 820

ground object -- no derivation owed

Rests on

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 definition 4.33 Vector space ¶
- 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 equation 5.173 eq:rep-symplectic-J ¶

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type	direction	node	provenance	where
`depends_on`	→	The symplectic group	declared	parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:1357
`depends_on`	→	eq:rep-symplectic-J	declared	parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:1357