query: Can there be an one dimensional vector space in $\mathbb{R}^3$ over $\mathbb{R}$ changing the usual operations of $\mathbb{R}^3$?
positive_passages.docid: 151425
positive_passages.text: Does $\mathbb{R}^n$ have a real vector space structure with dimension other than $n$?
negative_passages.docid: 68526
negative_passages.text: Polynomials as vector spaces?
negative_passages.docid: 94378
negative_passages.text: Is Linear transformations $T_1,T_2 : \mathbb{R}^n\rightarrow \mathbb{R}^n$ Invertible?
negative_passages.docid: 43282
negative_passages.text: Why do $n$ linearly independent vectors span $\mathbb{R}^{n}$?
negative_passages.docid: 74465
negative_passages.text: One-dimensional vector space and it's subspaces
negative_passages.docid: 4319
negative_passages.text: Vector space can be written as direct sum of subspaces
negative_passages.docid: 42883
negative_passages.text: Cross product in $\mathbb R^n$
negative_passages.docid: 60684
negative_passages.text: Determine whether the set $W$ is a subspace in $\mathbb{R}^{3}$
negative_passages.docid: 143517
negative_passages.text: Isomorphisms Between a Finite-Dimensional Vector Space and its Dual
negative_passages.docid: 122121
negative_passages.text: Is there a vector space that cannot be an inner product space?
negative_passages.docid: 18913
negative_passages.text: How to find a basis for the intersection of two vector spaces in $\mathbb{R}^n$?
negative_passages.docid: 29030
negative_passages.text: Vector space with new scalar multiplication defined over finite field still vector space?
negative_passages.docid: 37119
negative_passages.text: Determine Which of the following Sets is a Vector Space
negative_passages.docid: 132300
negative_passages.text: Dimensions of vector spaces in an exact sequence
negative_passages.docid: 112548
negative_passages.text: Existence of non-trivial linear functional on any vector space
negative_passages.docid: 12825
negative_passages.text: Bijection between $2^{\mathbb R}$ and $\mathbb{ R ^ R}$
negative_passages.docid: 72644
negative_passages.text: Continuous injective map $f:\mathbb{R}^3 \to \mathbb{R}$?