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 …

The definition of a subspace is a subset that itself is a vector space. The "rules" you know to be a subspace I'm guessing are 1) non-empty (or equivalently, containing the zero vector) 2) …

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 …

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 …

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 …

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 …

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).

Wiki says, subspace is a subset of a higher dimension space. Then we could just consider my example to be subspace of three-dimension vector space. And sorry, I didn't get the point of …