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Parents1

  • Coordinate vector spaces

Siblings11
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  • Algebraic properties of R^n (or C^n)
  • Geometric properties of R^n (or C^n)
  • Axioms of a vector space
  • Linear combinations
  • Spans
  • Subspaces
  • Linear (in)dependence
  • Bases
  • Dimension
  • Linear transformations
  • Orthogonality and projection

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  • Definition of dimension of a vector space (or subspace)
  • If a vector space has dimension n
  • Every basis for a vector space contains the same number of elements
  • Definition of dimension of a vector space (or subspace) being finite or infinite
  • The dimension of a subspace is less than or equal to the dimension of the whole space
  • If two finite dimensional subspaces have the same dimension and one is contained in the other
  • A set of vectors containing more elements than the dimension of the space must be linearly dependent
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