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  • Norm and length

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  • Definition of norm/length of a vector
  • Definition of unit vector
  • The inner product of a vector with itself is the square of its norm/length.
  • Definition of distance
  • The triangle inequality
  • The Cauchy–Schwarz inequality
  • Definition of length/norm of a vector
  • Definition of distance between vectors
  • The Cauchy-Schwarz inequality
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  1. The Cauchy–Schwarz inequality

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  • The Cauchy-Schwarz inequalityClose match
  • The triangle inequalityClose match
  • Norm and lengthClose match
  • Definition of angle between vectorsClose match
  • The inner product of a vector with itself is the square of its norm/length.Close match
  • Pythagorean equality characterizes orthogonality over the realsClose match
  • Geometric properties of R^n (or C^n)Close match
  • The standard inner product of a vector with itself is non-negativeClose match
  • The standard inner product of a vector with itself is 0 only for the 0 vectorClose match
  • Definition of norm/length of a vectorClose match
  • Definition of distanceClose match
  • Definition of length/norm of a vectorRelated
  • Inner products in coordinate spacesRelated
  • The complex inner product is conjugate symmetricRelated
  • A matrix with real entries and orthonormal columns preserves norms.Related
  • Inner productsRelated
  • OrthogonalityRelated
  • The standard inner product on R^n (or C^n) distributes over addition.Related
  • Definition of distance between vectorsRelated
  • Definition of unit vectorRelated

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