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 …
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?
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 …
What is the Role of Subspace in Sci-Fi Universes?
Dec 19, 2004 · Subspace is a term frequently used in science fiction, particularly in shows like Star Trek and Stargate, to describe a hypothetical dimension that allows for faster-than-light …
Determining if a set is a subspace. • Physics Forums
Oct 5, 2014 · I am trying to determine how to tell if a set is a subspace. The problem reads like this: Determine if the described set is a subspace. If so, give a proof. If not, explain why not. …
What are the properties to prove a plane is a subspace of R^3?
Sep 19, 2006 · I have a question that states: Let a, b, and c be scalers such that abc is not equal to 0. Prove that the plane ax + by + cz = 0 is a subspace of R^3.
Upper trianglar matrix is a subspace of mxn matrices
Oct 9, 2016 · Homework Statement Prove that the upper triangular matrices form a subspace of ##\\mathbb{M}_{m \\times n}## over a field ##\\mathbb{F}## Homework EquationsThe Attempt …
Why R2 is not a subspace of R3? - Physics Forums
Aug 25, 2006 · I think R2 is a subspace of R3 in the form (a,b,0)'.
Subspaces of R3: Proof or Counterexample • Physics Forums
Oct 13, 2008 · missed last week due to illness so have no clue what this homework is going on about, the question is for each of the following state whether or not it is a subspace of R3, …
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,