Dimension of a vector space and its subspaces - Physics Forums
Jan 24, 2024 · Can a vector subspace have the same dimension as the space it is part of? If so, can such a subspace have a Cartesian equation? if so, can you give an example. Thanks in advance;
Determining if a set is a subspace. • Physics Forums
Oct 5, 2014 · I am trying to determine how to tell if a set is a subspace. The problem reads like this: Determine if the described set is a subspace. If so, give a proof. If not, explain why not. Unless …
Is a subspace still valid without the zero vector? - Physics Forums
Jan 21, 2009 · No, because the subspace will have negatives of elements, i.e., for all v an element of V, (-1)v or -v will be an element. For the subspace to be closed under addition (a necessary …
What is the Role of Subspace in Sci-Fi Universes?
Dec 19, 2004 · Subspace is a term frequently used in science fiction, particularly in shows like Star Trek and Stargate, to describe a hypothetical dimension that allows for faster-than-light travel and …
Subspace vs Subset: Understanding the Relationship
Oct 13, 2025 · Hi, A quick question: Does a set need to be a subset to be a subspace of some vector space?
Why Does a Subset of a Vector Space Need the Zero Vector to Be a …
Feb 7, 2008 · I am curious as to why a subset of a vector space V must have the vector space V's zero vector be the subsets' zero vector in order to be a subspace. Its just not intuitive.
Linear Algebra: Prove that the set of invertible matrices is a Subspace
Jan 27, 2013 · Homework Statement Is U = {A| A \\in nℝn, A is invertible} a subspace of nℝn, the space of all nxn matrices? The Attempt at a Solution This is easy to prove if you assume the regular …
Why R2 is not a subspace of R3? - Physics Forums
Aug 25, 2006 · I think R2 is a subspace of R3 in the form (a,b,0)'.
Determining subspaces for all functions in a Vector space
Oct 14, 2015 · Homework Statement First, I'd like to say that this question is from an Introductory Linear Algebra course so my knowledge of vector space and subspace is limited. Now onto the question. Q: …
Distance from a vector to a subspace • Physics Forums
Nov 3, 2013 · Similar threads I Vector subspace and basis vectors in the context of data science Mar 17, 2024 Replies 6 Views 3K MHB -311.1.5.8 Ax=b in parametric vector form,