query: Why do we have vector spaces over a **field**?
positive_passages.docid: 19671
positive_passages.text: Does the "field" over which a vector space is defined have to be a Field?
negative_passages.docid: 158170
negative_passages.text: vector space dimension of linear varieties
negative_passages.docid: 70413
negative_passages.text: A vector space over $R$ is not a countable union of proper subspaces
negative_passages.docid: 59647
negative_passages.text: Vector spaces with fractional dimension
negative_passages.docid: 37119
negative_passages.text: Determine Which of the following Sets is a Vector Space
negative_passages.docid: 89058
negative_passages.text: Question on finite Vector Spaces, injective, surjective and if $V$ is not finite
negative_passages.docid: 141843
negative_passages.text: n-dimensional vector space isomorphic to the n-th product of a field as abelian groups
negative_passages.docid: 137873
negative_passages.text: Problems that involves two facts in the definition of vector spaces
negative_passages.docid: 53850
negative_passages.text: Proof that every normed vector space is a topological vector space
negative_passages.docid: 25039
negative_passages.text: Zero vector of a vector space
negative_passages.docid: 120475
negative_passages.text: Vector spaces - Multiplying by zero scalar yields zero vector
negative_passages.docid: 107389
negative_passages.text: Show that the vector space of real functions is not finitely spanned
negative_passages.docid: 60685
negative_passages.text: The vector space formed on C[0,1] and the norm $(\int_{0}^{1}|f(t)|^2 dt)^{1/2} $
negative_passages.docid: 116916
negative_passages.text: What's the rationale for requiring that a field be a $\boldsymbol{non}$-$\boldsymbol{trivial}$ ring?
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: 27478
negative_passages.text: Proof that two basis of a vector space have the same cardinality in the infinite-dimensional case
negative_passages.docid: 28402
negative_passages.text: Number of bases of an n-dimensional vector space over q-element field.