- Is a subspace still valid without the zero vector? - Physics Forums
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 requirement) v + (-v) = 0 must be an element which implies the zero vector must be in a subspace of vectors
- Determining if a set is a subspace. • Physics Forums
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 stated otherwise, a, b, and c are real numbers The subset of {R}^ {3} consisting of vectors of the form $$\left [\begin {array} {c}a \\ 0 \\ b \end {array
- What is the Role of Subspace in Sci-Fi Universes?
Subspace is a term frequently used in science fiction, particularly in shows like Star Trek and Stargate, to describe a hypothetical dimension that allows for faster-than-light travel and communication It is not a scientifically recognized concept but rather a literary device that facilitates plot developments involving wormholes and other space phenomena In scientific terms, subspace can
- Dimension of a vector space and its subspaces • Physics Forums
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;
- Subspace vs Subset: Understanding the Relationship
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
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 operations of vector addition and scalar multiplication Then the Identity matrix is in the set but 0*I and
- Why R2 is not a subspace of R3? - Physics Forums
I think R2 is a subspace of R3 in the form (a,b,0)'
- Finding Basis for Subspaces of R4 - Physics Forums
The discussion revolves around finding bases for subspaces W and U in R4 and determining their intersections and sums The basis for W is identified as a (1,1,1,0) + b (-1,2,0,1), leading to a homogeneous system of equations For W ∩ U, a comparison of the systems reveals a basis of (-0 5, 4, 1, 1 5) The basis for W + U is proposed as four vectors, but it is later clarified that they are
|