Why R2 is not a subspace of R3? - Physics Forums
Aug 25, 2006 · R^2 is isomorphic to the subset (a,b,0) of R^3, but it's also isomorphic to infinitely many other subspaces of R^3 (any 2 dimensional one). As such, there's no canonical embedding, …
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 idea …
Solving Vector Subspace Questions: A & B in V - Physics Forums
Mar 15, 2011 · Prove your answer. b) Determine whether or not A ∪ B is a vector subspace of V . Prove your answer. My strategy for this is to find two subspaces in V and find a counter claim so …
What is a Closed Linear Subspace? - Physics Forums
Jun 10, 2011 · Here's an example, "If L is a closed linear subspace of H, then the set of of all vectors in H that are orthogonal to every vector in L is itself a closed linear subspace". But 'closed linear …
Distance from a vector to a subspace - Physics Forums
Nov 3, 2013 · Similar threads I Vector subspace and basis vectors in the context of data science Mar 17, 2024 Replies 6 Views 3K MHB -311.1.5.8 Ax=b in parametric vector form,
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. . Since , then , …
Prove the sum of two subspaces is also a subspace.
Sep 6, 2009 · Homework Equations is a subspace of if is also a vector space and it contains the additive identity, is closed under addition, and closed under scalar multiplication. The definition of …
Subspace topology of Rationals on Reals - Physics Forums
Oct 31, 2012 · I am trying to visualize the subsppace topology that is generated when you take the Rationals as a subset of the Reals. So if we have ℝ with the standard topology, open sets in a …
How to determine the smallest subspace? - Physics Forums
Jan 23, 2016 · The smallest subspace containing vectors in the list is . How can one know how small a subspace is? initially I thought it was determined from the number of elements in the subspace, …
Dimension of a vector space and its subspaces - Physics Forums
Jan 24, 2024 · Can a vector subspace have the same dimension as the space it is part of? If so, can such a subspace have a Cartesian equation? if so, can you give an example. Thanks in advance;