Geometric Description of Subspace Spanned by Set S
Nov 5, 2014 · The geometric description of the subspace spanned by S is a plane defined by the vectors, specifically the subset of points where the second component is zero, represented as …
Why R2 is not a subspace of R3? • Physics Forums
Aug 25, 2006 · R^2 is not a subspace of R^3 because R^2 consists of vectors with two components, while R^3 consists of vectors with three components, making them …
Subspaces in R4: Get Started & Understand Now - Physics Forums
Mar 7, 2006 · W is defined as the set of vectors in R4 satisfying the equation x1 + x3 = x2 + x4, and it qualifies as a subspace of R4. To verify this, one must check the three main properties: …
Subspaces of R3: Proof or Counterexample • Physics Forums
Oct 13, 2008 · If W is a vector space itself, with the same vector space operations as V has, then it is a subspace of V. To use this definition, we don't have to prove that all the properties of a …
Show that a "cross" is not a topological manifold • Physics Forums
Jul 30, 2024 · Yes, that is (in bold) the point: "the cross" topological space is defined using the subspace topology from ##\mathbb R^2## standard topology. Yes, and the result holds under …
Subspaces of R2 and R3: Understanding Dimensions of Real …
Mar 4, 2008 · So I'm considering dimensions of real vector spaces. I found myself thinking about the following: So for the vector space R2 there are the following possible subspaces: 1. {0} 2. …
Proving Subspace of Mnn: AB=BA for Fixed nxn Matrix B
Sep 15, 2011 · Homework Statement Prove that the set of all n x n matrices A such that AB = BA for a fixed n x n matrix B, is a subspace of Mnn. Homework Equations u + v is in the same …
Is there a symbol for indicating one vector space is a subspace of ...
Apr 27, 2011 · Hi all, I was just wondering, is there is a particular symbol to say V is a subspace of W? I suppose V\subsetW works if I describe each (sub)space in...
Determining Polynomial Subspaces in P4 • Physics Forums
Sep 18, 2012 · The discussion focuses on determining which sets of polynomials in P4 qualify as subspaces. It is established that only the set of polynomials p (x) where p (0) = 0 is a …
Dimension of a vector space and its subspaces • Physics Forums
Jan 24, 2024 · My thought was that was a vector space and a subspace with an uncountably infinite index. I then confused index and dimension instead of building a correct counterexample.