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Bookmark or Share- 9.1: Subspaces - Mathematics LibreTextsDefinition: subspace. We say that a subset \(U\) of a vector space \(V\) is a \(\textit{subspace}\) of \(V\) if \(U\) is a vector space under the inherited addition and scalar multiplication operations of \(V\).
- 2.6: Subspaces - Mathematics LibreTextsWriting a subspace as a column space or a null space. A subspace can be given to you in many different forms. In practice, computations involving subspaces are much easier if your subspace is the column space or null space of a matrix.
- Linear subspace - WikipediaIn mathematics, and more specifically in linear algebra, a linear subspace or vector subspace is a vector space that is a subset of some larger vector space. A linear subspace is usually simply called a subspace when the context serves to distinguish it from other types of subspaces.
- 9.4: Subspaces and Basis - Mathematics LibreTextsA subset W ⊆ V is said to be a subspace of V if a→x + b→y ∈ W whenever a, b ∈ R and →x, →y ∈ W. The span of a set of vectors as described in Definition 9.2.3 is an example of a subspace. The following fundamental result says that subspaces are subsets of a vector space which are themselves vector spaces.
- Basis of a subspace (video) | Khan AcademyThe subspace defined by those two vectors is the span of those vectors and the zero vector is contained within that subspace as we can set c1 and c2 to zero. In summary, the vectors that define the subspace are not the subspace.
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