The main difference between refering to a vector spaces as a linear space or as a subspace is, unsurprisingly, context. When one talks about a "subspace", one is thinking of it as being …

Mar 31, 2014 · Can someone explain the difference between a subspace and a vector space? I realize that a vector space has 10 axioms that define how vectors can be added and …

I'm in a linear algebra class and am having a hard time wrapping my head around what subspaces of a vector space are useful for (among many other things!). My understanding of a …

According to this definition the subset $\ { (0,0); (0,1)\}$ is an affine subspace, while this is not so according to the usual definition of an affine subspace.

Jul 21, 2014 · Can you give the definition of subspace and subset of $\\mathbb{R}^n$ and how can I determine their dimension?

For a class I am taking, the proff is saying that we take a vector, and 'simply project it onto a subspace', (where that subspace is formed from a set of orthogonal basis vectors).

I have two subspaces: $$W_1 = \ { (x, 3x) : x\in \Bbb R \}$$ and $$W_2 = \ { (2x, 0): x\in \Bbb R \}$$ How do I get $W_1 + W_2$? I tried simply adding a sample vector ...

Dec 6, 2013 · Is there a proper notation for denoting subspaces? For example, if $U$ is a subspace of some vector space $V$. I would usually just write "the subspace $U \\subseteq ...

Nov 11, 2022 · A subspace of V V is a subset W W which is a vector space with respect to the same operations (addition and scalar multiplication) as V V, when they are restricted to W W.

But being a subspace means more than just being a subset. In addition, it requires the subset to possess the same kind of structure that the larger space does: in particular, to be closed under …