Some interesting linear algebra theories

  1. if U and W are subspaces for a vector space V then U \cap W is a subspace (of V ).
  2. Definition: \{U + W\} denotes the set of all the vectors possible to construct by adding a vector from U with a vector from W where U and W may be either set of vectors or subspace of vectors.
  3. If  U and W are subspaces for a vector space V then \{U + W\} is the smallest subspace which contain both U and W .
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