[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 …
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 …
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 ′ …
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 …
Proving Kernel of T is a Subspace of V - Physics Forums
May 21, 2014 · The discussion revolves around proving that the kernel of a linear transformation T from a vector space V to another vector space W is a subspace of V. Participants explore the definition of …
Is every subspace of a connected space connected? - Physics Forums
Aug 18, 2007 · The discussion centers around the question of whether every subspace of a connected space is itself connected, exploring concepts within general topology. Participants examine …
Orthogonal Projection Onto a Subspace? - Physics Forums
Aug 23, 2010 · The discussion focuses on calculating the orthogonal projection of a vector onto a subspace in linear algebra. The user initially struggles with the concept but receives clarification that …
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 …
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 …
Subspace Verification in R4: Homework Question & Solution
Dec 8, 2013 · The discussion revolves around verifying whether certain sets W are subspaces of R4. The sets are defined by specific conditions involving their components, and participants are tasked …