Showing that U = { (x, y) | xy ≥ 0} is not a subspace of R^2
2012年11月22日 · 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 …
Dimension of a vector space and its subspaces - Physics Forums
2024年1月24日 · 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 …
Subspaces of R3: Proof or Counterexample • Physics Forums
2008年10月13日 · 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 …
Is the Empty Set a Valid Vector Space? A Closer Look at the Ten Axioms ...
2005年8月3日 · 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 …
Why Does a Subset of a Vector Space Need the Zero Vector to Be a …
2008年2月7日 · 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 …
Showing that a set of differentiable functions is a subspace of R
2020年11月27日 · 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 …
A subset of R^ (2) that is a nontrivial subspace of R^ (2)
2016年3月31日 · 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 …
Determining Polynomial Subspaces in P4 • Physics Forums
2012年9月18日 · 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 …
Proving Subspace of Mnn: AB=BA for Fixed nxn Matrix B
2011年9月15日 · 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 …
How to determine the smallest subspace? - Physics Forums
2016年1月23日 · The smallest subspace containing vectors in the list is . How can one know how small a subspace is? initially I thought it was determined from the number of elements in the subspace, but …