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  • Orthogonality and projection

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  • Inner products in coordinate spaces
  • Norm and length
  • Orthogonality
  • Projection
  • Least squares
  • Inner products

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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. Norm and length

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  • The inner product of a vector with itself is the square of its norm/length.Close match
  • The triangle inequalityClose match
  • Definition of length/norm of a vectorClose match
  • Definition of norm/length of a vectorClose match
  • The standard inner product of a vector with itself is non-negativeClose match
  • The Cauchy-Schwarz inequalityClose match
  • Inner products in coordinate spacesClose match
  • Inner productsClose match
  • The Cauchy–Schwarz inequalityClose match
  • A matrix with real entries and orthonormal columns preserves norms.Close match
  • The standard inner product of a vector with itself is 0 only for the 0 vectorClose match
  • The standard inner product on R^n is commutative.Close match
  • Geometric properties of R^n (or C^n)Close match
  • Pythagorean equality characterizes orthogonality over the realsClose 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
  • Definition of distanceClose match
  • Definition of distance between vectorsClose match
  • OrthogonalityClose match
  • Definition of unit vectorClose match
  • Definition of orthogonal vectorsClose match

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