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 U = { (x, y) | xy ≥ 0} is not a subspace of R^2
Nov 22, 2012 · Understanding of vector spaces and their properties Study the properties that define a subspace in vector spaces Investigate the implications of vector addition in subsets Students …
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 …
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 …
What are the properties to prove a plane is a subspace of R^3?
Sep 19, 2006 · The discussion centers on proving that the plane defined by the equation ax + by + cz = 0 is a subspace of R^3, given that scalars a, b, and c are non-zero. The user initially misinterprets …
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?
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 …
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 …
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 …
Is the Empty Set a Valid Vector Space? A Closer Look at the Ten Axioms ...
Aug 3, 2005 · The discussion centers on whether the empty set can be considered a valid vector space. Participants assert that while the empty set is a subset of every set, it cannot satisfy the …