query: Is it true that a field is a vector space over a field?
positive_passages.docid: 151117
positive_passages.text: Are all fields vector spaces?
negative_passages.docid: 42046
negative_passages.text: How to tell if a set of vectors spans a space?
negative_passages.docid: 67191
negative_passages.text: When is the union of a family of subspaces of a vector space also a subspace?
negative_passages.docid: 81628
negative_passages.text: Why do we call a vector space in terms of vector space over some field?
negative_passages.docid: 61220
negative_passages.text: What does "$\mathbb{F^n}$ is a vector space over $\mathbb{F}$" mean?
negative_passages.docid: 123408
negative_passages.text: Why a subspace of a vector space is useful
negative_passages.docid: 126303
negative_passages.text: Are there linear operators and vector spaces in classical physics?
negative_passages.docid: 4319
negative_passages.text: Vector space can be written as direct sum of subspaces
negative_passages.docid: 5347
negative_passages.text: Using the definition of a vector space to prove that $0x = 0$ and $(-1)x = -x$
negative_passages.docid: 120475
negative_passages.text: Vector spaces - Multiplying by zero scalar yields zero vector
negative_passages.docid: 154724
negative_passages.text: Every vector space has a basis
negative_passages.docid: 146339
negative_passages.text: Proof of -(-v)=v in a vector space
negative_passages.docid: 60212
negative_passages.text: algebraic element over a field
negative_passages.docid: 36131
negative_passages.text: $\sigma$-algebra vs. $\sigma$-field: is there any difference?
negative_passages.docid: 38817
negative_passages.text: Why is the ring of matrices over a field simple?
negative_passages.docid: 90691
negative_passages.text: Linear independence of vectors over larger fields
negative_passages.docid: 141843
negative_passages.text: n-dimensional vector space isomorphic to the n-th product of a field as abelian groups