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  • Vector spaces

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  • Abstract vector spaces
  • Coordinate vector spaces
  • Examples of vector spaces

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  • The set containing only 0 is a vector space.
  • R^n is a vector space.
  • C^n is a vector space.
  • F^n is a vector space.
  • The set of all functions on a set is a vector space.
  • The solutions to a homogeneous system of linear equations is a vector space.
  • The solutions to a homogeneous linear differential equation is a vector space.
  • The set of all polynomials is a vector space.
  • The set of all polynomials of degree at most n is a vector space.
  • The set of m by n matrices is a vector space.
  • The set of all sequences is a vector space.
  • The crazy vector space is a vector space.
  • The row space of a matrix is a vector space
  • The column space of a matrix is a vector space
  • The null space of a matrix is a subspace of R^n (or C^n).
  • The left null space of a matrix is a subspace of R^m (or C^m).
  • The set of linear transformations between two vector spaces is a vector space.
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  1. Examples of vector spaces

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