equation 5.150 eq:lin-ctesesc2

open in the book · parts/02-mathematical-methods/03-linear-algebra-representations.tex:5316

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depends_on proposition 5.125 prop:lin-matrix-algebra ¶
- depends_on corollary 5.168 cor:rep-adjoint-faithful ¶
- depends_on definition 5.162 Representation of an algebra ¶
  - depends_on definition 5.163 Faithful, equivalent, invariant ¶
    - depends_on corollary 5.168 cor:rep-adjoint-faithful ¶ ↺
    - depends_on proposition 5.164 The kernel is an ideal ¶
      - depends_on corollary 5.168 cor:rep-adjoint-faithful ¶ ↺
  - depends_on proposition 5.167 Adjoint representation ¶
    - depends_on corollary 5.168 cor:rep-adjoint-faithful ¶ ↺
  - depends_on proposition 5.164 The kernel is an ideal ¶ ↺
- depends_on definition 9.21 Matrix exponential ¶
  - depends_on proposition 9.22 The exponential and its derivative ¶
    - depends_on theorem 9.23 Solution of a constant-coefficient system ¶
      - depends_on corollary 9.25 Normal modes of a diagonalizable system ¶
      - depends_on proposition 9.87 The distinguished limit, and which end carries the layer ¶
      - depends_on proposition 9.31 Lyapunov's first method: asymptotic stability ¶
      - depends_on proposition 9.43 The unmodulated line, and the feet of the tongues ¶
      - depends_on theorem 9.32 Hartman–Grobman; quoted ¶
      - depends_on theorem 9.26 Structure of the solutions ¶
- depends_on proposition 5.139 Dimension of the symplectic group ¶
  - depends_on proposition 24.5 Properties of the symplectic group ¶
    - depends_on remark 24.6 Connectedness, and what it rests on ¶
    - depends_on remark 24.7 Contrast with the orthogonal group ¶
  - depends_on remark 22.21 The count ¶
depends_on proposition 5.167 Adjoint representation ¶ ↺
step_from equation 5.157 eq:lin-cte-antisym ¶
step_from equation 5.158 eq:lin-cte-jacobi ¶
step_from equation 5.151 eq:lin-ctesesc3 ¶

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type	direction	node	provenance	where
`depends_on`	←	prop:lin-matrix-algebra	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:5360
`depends_on`	←	Adjoint representation	declared	parts/02-mathematical-methods/03-linear-algebra-representations.tex:7822
`step_from`	←	eq:lin-cte-antisym	declared — antisymmetry of the Lie bracket, written on a pair of basis elements	parts/02-mathematical-methods/03-linear-algebra-representations.tex:5486
`step_from`	←	eq:lin-cte-jacobi	declared — the Jacobi identity on basis elements, with the inner and outer brackets expanded in turn	parts/02-mathematical-methods/03-linear-algebra-representations.tex:5509
`step_from`	←	eq:lin-ctesesc3	declared — expand both arguments in the basis and replace the bracket of basis elements by the structure constants	parts/02-mathematical-methods/03-linear-algebra-representations.tex:5333