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?
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 …
[Linear Algebra] Show that H ∩ K is a subspace of V
Apr 28, 2018 · Homework Statement From Linear Algebra and Its Applications, 5th Edition, David Lay Chapter 4, Section 1, Question 32 Let H and K be subspaces of a vector space V. The …
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.
Determine if S is a subspace of V - Physics Forums
Feb 13, 2014 · My answers aren't all correct and I am not sure why.. Problem: Determine whether the given set S is a subspace of the vector space V. A. V is the vector space of all real-valued …
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 …
2-sphere intrinsic definition by gluing disks' boundaries
Aug 6, 2025 · Basically one starts assigning each disk the subspace topology from R 2 and then taking the quotient topology obtained by gluing their boundaries. Starting from the above …
Orthogonal Projection Onto a Subspace? - Physics Forums
Aug 23, 2010 · What he has calculated is the "shadow" of w on the subspace which is what he apparently meant by the orthogonal projection onto the subspace. What I suggested to you …
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 …
Closed subspace of a Lindelöf space is Lindelöf - Physics Forums
Jul 6, 2012 · I'm looking at Rao: Topology, Proposition 1.5.4, "A closed subspace of a Lindelöf space is Lindelöf." He gives a proof, which seems clear enough, using the idea that for each …