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 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 ...
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 ...
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.
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.
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...
Help with linear algebra: vectorspace and subspace Mar 16, 2021 Replies 15 Views 3K Finding the dimension of a subspace Dec 22, 2020 Replies 7 Views 2K Linear Algebra - Finding coordinates of a set
Similar threads I Vector subspace and basis vectors in the context of data science Mar 17, 2024 Replies 6 Views 3K MHB -311.1.5.8 Ax=b in parametric vector form,
