Subspaces of R3: Proof or Counterexample • Physics Forums
Oct 13, 2008 · The discussion centers on determining whether specific subsets of R3 are subspaces, based on the conditions provided. The three conditions analyzed are (i) a + b = c, …
Dimension of a vector space and its subspaces - Physics Forums
Jan 24, 2024 · A vector subspace can indeed have the same dimension as the vector space it is part of, specifically when the vector space is infinite-dimensional. In such cases, the subspace …
Why Does a Subset of a Vector Space Need the Zero Vector to Be …
Feb 7, 2008 · If each subspace has its own zero vector, then combine these subspaces in order to get a bigger subspace or even the whole space. We will get bunch of different zeros and the …
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?
A subset of R^ (2) that is a nontrivial subspace of R^ (2)
Mar 31, 2016 · The discussion centers on identifying a nontrivial subspace of R², specifically the subset defined by the equation { (x,y) ∈ R² : y = ax, a ∈ R - {0} }. Participants clarify that a …
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 …
Show that a "cross" is not a topological manifold - Physics Forums
Jul 30, 2024 · The discussion centers on the classification of a "cross" in the plane as a non-topological manifold. Participants agree that when the cross is given the subspace topology …
Subspaces in R4: Get Started & Understand Now - Physics Forums
Mar 7, 2006 · Practice proving subspace properties with various vector sets Students of linear algebra, educators teaching vector space concepts, and anyone seeking to understand the …
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 …
What are the properties to prove a plane is a subspace of R^3?
Sep 19, 2006 · The discussion centers on proving that the plane defined by the equation ax + by + cz = 0 is a subspace of R^3, given that scalars a, b, and c are non-zero. The user initially …