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 …
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. …
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 …
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?
Why Does a Subset of a Vector Space Need the Zero Vector to Be …
Feb 7, 2008 · I am curious as to why a subset of a vector space V must have the vector space V's zero vector be the subsets' zero vector in order to be a subspace. Its just not intuitive.
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 …
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)'.
Why Vector Spaces Explain The World: A Historical Perspective
Mar 13, 2025 · When he published a new, revised edition of this book in 1862, he was already much closer to his goal: the concepts of linear combination of linearly independent quantities, …
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 …