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 is referred to …
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, (ii) ab = c + 1, and …
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 Students …
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 · 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 whole space …
Is the Empty Set a Valid Vector Space? A Closer Look at the Ten Axioms ...
Aug 3, 2005 · The discussion centers on whether the empty set can be considered a valid vector space. Participants assert that while the empty set is a subset of every set, it cannot satisfy the …
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 nontrivial …
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 …
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 properties of …
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 ...