proposition 29.22 Perpendicular-axis theorem

Rests on

• depends_on definition 29.13 Inertia tensor, continuum form ¶
  • depends_on definition 7.125 Multiple integral ¶
    • depends_on axiom 7.1 Completeness of $\R$ ¶
    • depends_on definition 7.39 Darboux sums and the definite integral ¶
      • depends_on axiom 7.1 Completeness of $\R$ ¶ ↺
  • depends_on definition 13.5 Tensor under orthogonal transformations ¶
    • depends_on definition 13.4 Orthogonal coordinate transformation ¶
      • depends_on definition 13.3 Orthogonal coordinate system ¶
  • depends_on definition 19.42 Inertia tensor ¶
    • depends_on definition 13.5 Tensor under orthogonal transformations ¶ ↺
    • depends_on definition 19.41 Moment of inertia about an axis ¶
      • depends_on definition 19.39 Body ¶
        • depends_on definition 18.4 Body ¶
        • depends_on definition 19.3 Mass ¶
      • depends_on definition 19.3 Mass ¶ ↺
• depends_on proposition 29.17 Triangle inequalities ¶
  • depends_on theorem 29.16 Principal axes ¶
    • depends_on definition 29.13 Inertia tensor, continuum form ¶ ↺
    • depends_on proposition 29.15 Positivity ¶
      • depends_on definition 29.13 Inertia tensor, continuum form ¶ ↺
      • proves proof ch:12-rigid-body-rotating-frames@proof-9 ¶
    • depends_on theorem 5.79 Spectral theorem for a self-adjoint operator ¶
      • depends_on corollary 5.72 Existence of an eigenvalue over $\C$ ¶
        • depends_on theorem 8.19 Fundamental theorem of algebra ¶
        • depends_on theorem 5.71 The eigenvalues are the roots of the characteristic polynomial ¶
        • proves proof ch:03-linear-algebra-representations@proof-27 ¶
      • depends_on definition 5.41 Adjoint ¶
        • depends_on definition 5.18 Inner product ¶
        • depends_on definition 5.37 Linear transformation ¶
      • depends_on theorem 5.40 Rank–nullity ¶
        • depends_on definition 5.15 Basis ¶
        • depends_on definition 5.39 Kernel, image, nullity, rank ¶
        • depends_on lemma 5.38 Exchange and completion ¶
        • proves proof ch:03-linear-algebra-representations@proof-13 ¶
      • proves proof ch:03-linear-algebra-representations@proof-31 ¶
    • proves proof ch:12-rigid-body-rotating-frames@proof-10 ¶
  • proves proof ch:12-rigid-body-rotating-frames@proof-11 ¶
• proves proof ch:12-rigid-body-rotating-frames@proof-14 ¶

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