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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 inner product of a vector with itself is the square of its norm/length.

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  • Norm and lengthClose match
  • The standard inner product of a vector with itself is non-negativeClose match
  • Definition of length/norm of a vectorClose match
  • The triangle inequalityClose match
  • Definition of norm/length of a vectorClose match
  • The standard inner product of a vector with itself is 0 only for the 0 vectorClose match
  • Inner productsClose match
  • The Cauchy-Schwarz inequalityClose match
  • Definition of inner productClose match
  • The standard inner product on R^n is commutative.Close match
  • Inner products in coordinate spacesClose match
  • The standard inner product on C^n can be written as the product of a vector and the adjoint of a vector.Close match
  • The standard inner product on R^n commutes with (real) scalar multiplication.Close match
  • The standard inner product on R^n can be written as the product of a vector and the transpose of a vector.Close match
  • Definition of distance between vectorsClose match
  • Definition of inner/dot product on R^nClose match
  • Definition of inner/dot product on C^nClose match
  • The Cauchy–Schwarz inequalityClose match
  • The standard inner product on R^n (or C^n) distributes over addition.Close match
  • Pythagorean equality characterizes orthogonality over the realsClose match

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