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 …
Subspaces of R3: Proof or Counterexample • Physics Forums
Oct 13, 2008 · The discussion revolves around determining whether certain sets are subspaces of R³, with specific conditions provided for each set. Participants are exploring the definitions and …
A subset of R^ (2) that is a nontrivial subspace of R^ (2)
Mar 31, 2016 · The discussion revolves around identifying a nontrivial subspace of $\Bbb R^2$. Participants explore definitions, examples, and properties of subspaces in the context of vector …
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 …
Showing that a set of differentiable functions is a subspace of R
Nov 27, 2020 · Discussion Overview The discussion revolves around the problem of demonstrating that a specific set of differentiable real-valued functions on the interval (4, 4), defined by the condition f ′ …
Definition of a Degenerate Subspace (QM) • Physics Forums
Mar 26, 2020 · So Degenerate subspace is a subspace of the eigenspace of a certain Hermitian operator? In that case, Degenerate subspace is the space of degenerate eigenfunctions …
[Linear Algebra] Show that H ∩ K is a subspace of V
Apr 28, 2018 · The problem involves demonstrating that the intersection of two subspaces, H and K, of a vector space V, is itself a subspace of V. Additionally, an example in ℝ² is requested to illustrate that …
Is there a symbol for indicating one vector space is a subspace of ...
Apr 27, 2011 · The discussion centers on the notation used to indicate that one vector space, V, is a subspace of another vector space, W. While the set notation V ⊆ W is commonly accepted, …
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 …