example 12.25 Orthogonal polynomials

Rests on

• depends_on example 12.11 The function space $L^{2}$ ¶
  • depends_on definition 12.2 Hilbert space ¶
    • depends_on definition 5.18 Inner product ¶
      • 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 6.27 Convergence; Cauchy sequence; completeness ¶
      • depends_on definition 6.24 Metric ¶
        • depends_on definition 3.43 Map ¶
        • depends_on definition 3.38 Ordered pair and Cartesian product ¶
    • depends_on equation 5.44 eq:lin-norm-assoc ¶
  • depends_on definition 5.18 Inner product ¶ ↺
• depends_on proposition 12.23 Gram–Schmidt in a Hilbert space ¶
  • depends_on definition 5.27 Orthonormal basis ¶
    • depends_on definition 5.26 Orthogonal basis ¶
      • 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 5.24 Orthogonal vectors ¶
        • depends_on definition 5.18 Inner product ¶ ↺
    • depends_on definition 5.25 Unit vector ¶
      • depends_on definition 5.19 Norm ¶
        • depends_on definition 4.33 Vector space ¶ ↺
  • depends_on proposition 5.28 Gram–Schmidt ¶
    • depends_on definition 5.14 Linear independence ¶ ↺
    • depends_on definition 5.18 Inner product ¶ ↺
    • depends_on definition 5.27 Orthonormal basis ¶ ↺
    • depends_on equation 5.44 eq:lin-norm-assoc ¶ ↺
    • proves proof ch:03-linear-algebra-representations@proof-5 ¶
  • proves proof ch:10-hilbert-spaces@proof-12 ¶

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