query: Every Vector Space is Regarded as a Vector Space Over a Given Field.
positive_passages.docid: 81628
positive_passages.text: Why do we call a vector space in terms of vector space over some field?
negative_passages.docid: 58424
negative_passages.text: If $A$ an integral domain contains a field $K$ and $A$ over $K$ is a finite-dimensional vector space, then $A$ is a field.
negative_passages.docid: 152325
negative_passages.text: Every subspace of the dual of a finite-dimensional vector space is an annihilator
negative_passages.docid: 124042
negative_passages.text: Why is a vector space equal to its tangent space for any point?
negative_passages.docid: 57310
negative_passages.text: Prove $\mathbb{Z}$ is not a vector space over a field
negative_passages.docid: 42362
negative_passages.text: Show that the dual space of the vector space of all polynomials is isomorphic to the infinite-dimensional Euclidean vector space over the reals
negative_passages.docid: 51397
negative_passages.text: If a field $F$ is such that $\left|F\right|>n-1$ why is $V$ a vector space over $F$ not equal to the union of $n$ proper subspaces of $V$
negative_passages.docid: 17
negative_passages.text: First Order Language for vector spaces over fields
negative_passages.docid: 84830
negative_passages.text: Vector space of infinite sequences in $\Bbb R$
negative_passages.docid: 83009
negative_passages.text: Showing that $R(x)$ is a proper subset of $R((x))$ if $R$ is a field
negative_passages.docid: 4151
negative_passages.text: Every subspace of a vector space has a complement
negative_passages.docid: 45252
negative_passages.text: "Every linear mapping on a finite dimensional space is continuous"
negative_passages.docid: 86362
negative_passages.text: Cyclic vectors in a real vector space
negative_passages.docid: 92510
negative_passages.text: Proving a vector space is infinite-dimensional
negative_passages.docid: 102371
negative_passages.text: Proving that two vector spaces of equal dimension are isomorphic
negative_passages.docid: 125073
negative_passages.text: Finite-dimensional subspaces of normed vector spaces are direct summands
negative_passages.docid: 130466
negative_passages.text: Proving every prime ideal is maximal in a finite dimensional ring over a field.