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 …
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 …
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. …
Show that a "cross" is not a topological manifold - Physics Forums
Jul 30, 2024 · Hi, I've a doubt about the following example in "Introduction to Manifold" by L. Tu. My understanding is that if one assumes the subspace topology from ##\\mathbb R^2## for …
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 …
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?
What are the properties to prove a plane is a subspace of R^3?
Sep 19, 2006 · I have a question that states: Let a, b, and c be scalers such that abc is not equal to 0. Prove that the plane ax + by + cz = 0 is a subspace of R^3.
Why Does a Subset of a Vector Space Need the Zero Vector to Be …
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.
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)'.
Finding Basis for Subspaces of R4 - Physics Forums
Jan 29, 2009 · Formulation of a proof of subspaces Jan 22, 2019 Replies 10 Views 2K T is cyclic iff there are finitely many T-invariant subspace Oct 18, 2018 Replies 4 Views 3K Linear …