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 …

Apr 10, 2016 · Eigenspaces are subspaces. Spans are subspaces. Orthogonal complements are subspaces. If you have a linear transformation between vector spaces, the image of a …

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 …

Nov 11, 2022 · I have seen people give the definition that a subspace is a vector space contained within a vector space. But is this definition actually accurate? Isn't this a special case, in …

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 …

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?

Sep 14, 2018 · I am reading these two sections of text: and Why is there an emphasis on nonempty? Isn't that by definition always true? According to these two pieces of text, a …

I am trying to understand how - exactly - I go about projecting a vector onto a subspace. Now, I know enough about linear algebra to know about projections, dot products, spans, etc etc, so I …