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 …
Showing that U = { (x, y) | xy ≥ 0} is not a subspace of R^2
Nov 22, 2012 · Understanding of vector spaces and their properties Study the properties that define a subspace in vector spaces Investigate the implications of vector addition in subsets …
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 …
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 …
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 …
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 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 …
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 …
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 …
How to find a basis of a subspace V = { (x1; x2;….; xn) | Σni=1 xi=0 ...
Sep 13, 2009 · The discussion focuses on finding a basis for the subspace V = { (x1; x2;….; xn) | Σni=1 xi=0} in Rn, where the sum of the vectors equals zero. For n=2, the basis ...