proposition 5.136 $\Sp(2n,\R)$ is a subgroup of $\GL(2n,\R)$

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 5.81 eq:lin-GL-matrices ¶
• depends_on proposition 5.48 Existence, uniqueness, and linearity of the inverse ¶
  • depends_on definition 5.47 Inverse of a linear transformation ¶
    • depends_on definition 5.37 Linear transformation ¶ ↺
  • depends_on definition 5.37 Linear transformation ¶ ↺
  • proves proof ch:03-linear-algebra-representations@proof-17 ¶
• proves proof ch:03-linear-algebra-representations@proof-59 ¶

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