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  • 7.5: Subspaces
    https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/07%3A_Vector_Spaces/7.05%3A_Subspaces
    In this section we will examine the concept of subspaces introduced earlier in terms of Rn. Here, we will discuss these concepts in terms of abstract vector spaces.
  • 2.6: Subspaces
    https://math.libretexts.org/Bookshelves/Linear_Algebra/Interactive_Linear_Algebra_(Margalit_and_Rabinoff)/02%3A_Systems_of_Linear_Equations-_Geometry/2.06%3A_Subspaces
    This page defines subspaces in Rn and outlines criteria for a subset to qualify as a subspace, including non-emptiness and closure under addition and scalar multiplication. It offers exa...This page defines subspaces in Rn and outlines criteria for a subset to qualify as a subspace, including non-emptiness and closure under addition and scalar multiplication. It offers examples of valid and invalid subspaces, discusses conditions specific to R2, and explains spanning sets of subspaces, particularly the column and null spaces of matrices.
  • 7.6: Basis
    https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/07%3A_Vector_Spaces/7.06%3A_Basis
    In this section we extend a linearly independent set and shrink a spanning set to a basis of a given vector space.

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