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  • Coordinate vector spaces

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  • Algebraic properties of R^n (or C^n)
  • Axioms of a vector space
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  • Linear (in)dependence
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  • Dimension
  • Linear transformations
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  • Geometric properties of R^n (or C^n)
  • Orthogonality and projection

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  • Example of a sum of vectors interpreted geometrically in R^2
  • Vector sum/addition interpreted geometrically in R^n (or C^n)
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  1. Geometric properties of R^n (or C^n)

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  • Algebraic properties of R^n (or C^n)Close match
  • Definition of R^n (or C^n)Close match
  • R^n is a vector space.Close match
  • Vector sum/addition interpreted geometrically in R^n (or C^n)Close match
  • The standard inner product on R^n is commutative.Close match
  • Inner products in coordinate spacesClose match
  • Geometric properties of linear transformations on R^2Close match
  • Example of a sum of vectors interpreted geometrically in R^2Close match
  • C^n is a vector space.Close match
  • The standard inner product on R^n commutes with (real) scalar multiplication.Close match
  • Definition of vectorClose match
  • Inner productsClose match
  • Norm and lengthClose match
  • Coordinate vector spacesClose match
  • Definition of inner/dot product on R^nClose 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 norm/length of a vectorClose 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
  • The standard inner product on R^n (or C^n) distributes over addition.Close match
  • Example of vector-scalar multiplication in R^2Close match

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