query: Is there a vector space with a non-trivial zero vector?
positive_passages.docid: 25039
positive_passages.text: Zero vector of a vector space
negative_passages.docid: 74465
negative_passages.text: One-dimensional vector space and it's subspaces
negative_passages.docid: 52865
negative_passages.text: Topological Vector Space: $\dim Z\text{ finite}\implies Z\text{ closed}$
negative_passages.docid: 151752
negative_passages.text: Example of a linear operator on some vector space with more than one right inverse.
negative_passages.docid: 154724
negative_passages.text: Every vector space has a basis
negative_passages.docid: 1162
negative_passages.text: Why $\{\mathbf{0}\}$ has dimension zero?
negative_passages.docid: 143517
negative_passages.text: Isomorphisms Between a Finite-Dimensional Vector Space and its Dual
negative_passages.docid: 1799
negative_passages.text: How many k-dimensional subspaces there are in n-dimensional vector space over $\mathbb F_p$?
negative_passages.docid: 66283
negative_passages.text: Let V be a vector space. If every subspace of V is T-invariant, prove that there exist a scalar multiple c such that T=c1v
negative_passages.docid: 151425
negative_passages.text: Does $\mathbb{R}^n$ have a real vector space structure with dimension other than $n$?
negative_passages.docid: 86362
negative_passages.text: Cyclic vectors in a real vector space
negative_passages.docid: 91022
negative_passages.text: How do I prove that a subspace of a vector space $X$ is the null space of some linear functional on $X$?
negative_passages.docid: 8902
negative_passages.text: Can Gaussian elimination find a zero vector when $m < n$?
negative_passages.docid: 120535
negative_passages.text: Basis of the polynomial vector space
negative_passages.docid: 34520
negative_passages.text: Is $0\,\mathrm{m}$ dimensionless?
negative_passages.docid: 92510
negative_passages.text: Proving a vector space is infinite-dimensional
negative_passages.docid: 117986
negative_passages.text: Are there linear transformations from vector spaces over different fields?