Jan 24, 2024 · My thought was that was a vector space and a subspace with an uncountably infinite index. I then confused index and dimension instead of building a correct counterexample.

Mar 4, 2008 · So I'm considering dimensions of real vector spaces. I found myself thinking about the following: So for the vector space R2 there are the following possible subspaces: 1. {0} 2. …

Mar 7, 2006 · I'm so lost! 1. W is the set of all vectors in R4 such that x1 + x3 = x2 + x4. Is W a subspace of R4 and Why? How do i get started here? I'm thoroughly confused on this whole …

Feb 28, 2008 · Every non-empty subset W of a vector space V over the field F2 is a subspace if it is closed under addition. To confirm W is a subspace, it must also be closed under scalar …

Oct 13, 2008 · If W is a vector space itself, with the same vector space operations as V has, then it is a subspace of V. To use this definition, we don't have to prove that all the properties of a …

Apr 27, 2011 · There is no universally accepted symbol to indicate that one vector space is a subspace of another. While V ⊆ W is commonly used in set notation, some prefer the notation …

Mar 7, 2009 · My understanding of the subspace still isn't solid enough, so I want to know what I know so far is at least correct. By definition, a set of vectors S of Rn is called a subspace of Rn …

Feb 25, 2008 · Homework Statement Determine whether the following is a subspace of P_ {4}_ (a) The set of polynomials in P_ {4} of even degree. Homework Equations...

Sep 15, 2011 · Homework Statement Prove that the set of all n x n matrices A such that AB = BA for a fixed n x n matrix B, is a subspace of Mnn. Homework Equations u + v is in the same …

Aug 3, 2005 · However, the empty set does span the vector space consisting of the zero vector, according to the definition of span: The span of a set of vectors is the smallest subspace …