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 …
Dimension of a vector space and its subspaces • Physics Forums
Jan 24, 2024 · Can a vector subspace have the same dimension as the space it is part of? If so, can such a subspace have a Cartesian equation? if so, can you give an example. Thanks in advance;
Determining if a set is a subspace. • Physics Forums
Oct 5, 2014 · I am trying to determine how to tell if a set is a subspace. The problem reads like this: Determine if the described set is a subspace. If so, give a proof. If not, explain why not. Unless …
Is there a symbol for indicating one vector space is a subspace of ...
Apr 27, 2011 · Hi all, I was just wondering, is there is a particular symbol to say V is a subspace of W? I suppose V\subsetW works if I describe each (sub)space in...
Proving Subspace of Mnn: AB=BA for Fixed nxn Matrix B
Sep 15, 2011 · Homework Statement Prove that the set of all n x n matrices A such that AB = BA for a fixed n x n matrix B, is a subspace of Mnn. Homework Equations...
Determine whether or not something is a subspace - Physics Forums
Mar 7, 2009 · My understanding of the subspace still isn't solid enough, so I want to know what I know so far is at least correct. By definition, a set of vectors S of Rn is called a subspace of Rn iff for all …
Show that a line in R2 is a subspace - Physics Forums
Mar 11, 2014 · Homework Statement Show that a line in R2 is a subspace if and only if it passes through the origin (0,0) The Attempt at a Solution Let A set of vectors be the subset of the vector …
Why Does a Subset of a Vector Space Need the Zero Vector to Be a …
Feb 7, 2008 · I am curious as to why a subset of a vector space V must have the vector space V's zero vector be the subsets' zero vector in order to be a subspace. Its just not intuitive.
Is a subspace still valid without the zero vector? - Physics Forums
Jan 21, 2009 · No, because the subspace will have negatives of elements, i.e., for all v an element of V, (-1)v or -v will be an element. For the subspace to be closed under addition (a necessary …
Why R2 is not a subspace of R3? - Physics Forums
Aug 25, 2006 · I think R2 is a subspace of R3 in the form (a,b,0)'.