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 …
Showing that a set of differentiable functions is a subspace of R
Nov 27, 2020 · Problem: Show that the set of differentiable real-valued functions on the interval such that is a subspace of This is my first bouts with rigorous mathematics and my brain is not at all wired …
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 …
Subspaces of R3: Proof or Counterexample • Physics Forums
Oct 13, 2008 · The discussion centers on determining whether specific subsets of R3 are subspaces, based on the conditions provided. The three conditions analyzed are (i) a + b = c, (ii) ab = c + 1, and …
[Linear Algebra] Show that H ∩ K is a subspace of V
Apr 28, 2018 · The discussion focuses on proving that the intersection of two subspaces H and K of a vector space V, denoted as H ∩ K, is itself a subspace of V. Participants reference Theorem 1 from …
A subset of R^ (2) that is a nontrivial subspace of R^ (2)
Mar 31, 2016 · The discussion centers on identifying a nontrivial subspace of R², specifically the subset defined by the equation { (x,y) ∈ R² : y = ax, a ∈ R - {0} }. Participants clarify that a nontrivial …
Proving Subspace of Mnn: AB=BA for Fixed nxn Matrix B
Sep 15, 2011 · The discussion centers on proving that the set of all n x n matrices A such that AB = BA for a fixed n x n matrix B forms a subspace of the vector space Mnn. The key points include the …
Determining Polynomial Subspaces in P4 • Physics Forums
Sep 18, 2012 · Ability to analyze polynomial expressions and their coefficients. Study the properties of vector spaces, focusing on subspace criteria. Learn about polynomial functions and their degrees in …
Why R2 is not a subspace of R3? - Physics Forums
Aug 25, 2006 · The three criteria for a subspace—containing the zero vector, closure under addition, and closure under scalar multiplication—highlight that R² is not a subset of R³ without a defined …
How do I determine if a set is a subspace? • Physics Forums
Oct 31, 2008 · To determine if a set is a subspace, it is essential to verify three criteria: the presence of the zero vector, closure under scalar multiplication, and closure under vector addition. The …