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  • Dimension

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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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  1. The dimension of a subspace is less than or equal to the dimension of the whole space

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