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.
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. …
Subspaces in R4: Get Started & Understand Now - Physics Forums
Mar 7, 2006 · I'm so lost! 1. W is the set of all vectors in R4 such that x1 + x3 = x2 + x4. Is W a subspace of R4 and Why? How do i get started here? I'm thoroughly confused on this whole …
Subspaces in Vector Spaces over F2 - Physics Forums
Feb 28, 2008 · Every non-empty subset W of a vector space V over the field F2 is a subspace if it is closed under addition. To confirm W is a subspace, it must also be closed under scalar …
Proving S is a Subspace of P2: A Scientific Approach
Aug 18, 2012 · Homework Statement Let S = { p \\in P_{2}(ℝ) | p(7) = 0 } Prove that S is a subspace of P_{2}(ℝ) (the vector space of all polynomials of degree at most 2) The Attempt at …
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 …
Showing that a set of differentiable functions is a subspace of R
Nov 27, 2020 · A few things; the subspace is also a space of functions, and the requirement of a zero vector in this context means that the subspace must contain a zero function , i.e. .
Is there a symbol for indicating one vector space is a subspace of ...
Apr 27, 2011 · There is no universally accepted symbol to indicate that one vector space is a subspace of another. While V ⊆ W is commonly used in set notation, some prefer the notation …
Subspace of P4: Polynomials of Even Degree • Physics Forums
Feb 25, 2008 · Homework Statement Determine whether the following is a subspace of P_ {4}_ (a) The set of polynomials in P_ {4} of even degree. Homework Equations...
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 …