query: non-zero Vector space with new scalar multiplication defined over finite field still vector space?
positive_passages.docid: 29030
positive_passages.text: Vector space with new scalar multiplication defined over finite field still vector space?
negative_passages.docid: 26989
negative_passages.text: Show that C[0,1] is a vector space
negative_passages.docid: 129476
negative_passages.text: The trace map in a finite field.
negative_passages.docid: 68526
negative_passages.text: Polynomials as vector spaces?
negative_passages.docid: 52596
negative_passages.text: A basis for $k(X)$ regarded as a vector space over $k$
negative_passages.docid: 129810
negative_passages.text: What kind of vector spaces have exactly one basis?
negative_passages.docid: 98391
negative_passages.text: example of a nonempty subset is closed under scalar multiplication but not a subspace
negative_passages.docid: 115129
negative_passages.text: Constructing an explicit isomorphism between finite extensions of finite fields
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: 5893
negative_passages.text: On the commutative property of multiplication (domain of integers, possibly reals)
negative_passages.docid: 34206
negative_passages.text: Quadratic form under $\mathbb{C}$ finite-dimension vector space always have a nonzero vector that yields zero?
negative_passages.docid: 151117
negative_passages.text: Are all fields vector spaces?
negative_passages.docid: 83586
negative_passages.text: Finite fields and primitive elements
negative_passages.docid: 35286
negative_passages.text: number of differents vector space structures over the same field $\mathbb{F}$ on an abelian group
negative_passages.docid: 51770
negative_passages.text: Number of elements in a finite field extension for finite fields
negative_passages.docid: 116823
negative_passages.text: VERIFYING: Proving an $n \times n$ Matrix Vector Space
negative_passages.docid: 28402
negative_passages.text: Number of bases of an n-dimensional vector space over q-element field.