Dimension of a vector space and its subspaces - Physics Forums
Jan 24, 2024 · A vector subspace can indeed have the same dimension as the vector space it is part of, specifically when the vector space is infinite-dimensional. In such cases, the subspace is referred to …
Why Does a Subset of a Vector Space Need the Zero Vector to Be a …
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 whole space …
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?
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 travel and …
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 necessary …
Subspaces in R4: Get Started & Understand Now - Physics Forums
Mar 7, 2006 · Practice proving subspace properties with various vector sets Students of linear algebra, educators teaching vector space concepts, and anyone seeking to understand the properties of …
How to find a basis of a subspace V = { (x1; x2;….; xn) | Σni=1 xi=0 ...
Sep 13, 2009 · The discussion focuses on finding a basis for the subspace V = { (x1; x2;….; xn) | Σni=1 xi=0} in Rn, where the sum of the vectors equals zero. For n=2, the basis ...
Linear Algebra: Prove that the set of invertible matrices is a Subspace
Jan 27, 2013 · Homework Statement Is U = {A| A \\in nℝn, A is invertible} a subspace of nℝn, the space of all nxn matrices? The Attempt at a Solution This is easy to prove if you assume the regular …
Subspace of P4: Polynomials of Even Degree • Physics Forums
Feb 25, 2008 · The set of polynomials of even degree within the vector space P 4 is not a subspace. This conclusion is drawn from the fact that the zero polynomial, which is of degree 0, is not included …
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.