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Linear subspaces with shading

A line and two planes passing through the origin in the three-dimensional vector space R3. All of them are subspaces of R3, and the line is also a subspace of the two planes.

A vector subspace or linear subspace is a vector space within a higher-dimensional vector space. A vector space W is a subspace of the vector space V over the field K if and only if:

  • The zero vector exists in W
  • The vectors v and u exist in W, v + u also exists in W (closed under vector addition)
  • If v is in W and c is a scalar in K, cv is in W

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