query: The dimension of $X$ as an affine variety is the same as the dimension as a vector space?
positive_passages.docid: 158170
positive_passages.text: vector space dimension of linear varieties
negative_passages.docid: 19671
negative_passages.text: Does the "field" over which a vector space is defined have to be a Field?
negative_passages.docid: 82824
negative_passages.text: Affine algebraic subset of $\mathbb{A}_k^4$
negative_passages.docid: 154724
negative_passages.text: Every vector space has a basis
negative_passages.docid: 155828
negative_passages.text: How do I show that $A$ and $A^T$ are similar, given that the minimal polynomial of $A$ splits over $\mathbb{F}$?
negative_passages.docid: 52596
negative_passages.text: A basis for $k(X)$ regarded as a vector space over $k$
negative_passages.docid: 99707
negative_passages.text: free module implies surjective map of affine schemes
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: 92291
negative_passages.text: $U_1, U_2, ..., U_k$ subspaces of linear space $X$ with same dimensions, prove $X=U_1\oplus V=U_2\oplus V=...=U_k\oplus V$
negative_passages.docid: 47266
negative_passages.text: Every affine variety in $\mathbb A^n$ consisting of finitely many points can be written as the zero locus of $n$ polynomials
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: 100340
negative_passages.text: Invariant dimension property on a ring without zero divisors
negative_passages.docid: 92510
negative_passages.text: Proving a vector space is infinite-dimensional
negative_passages.docid: 151161
negative_passages.text: norms on vector space are equivalent iff they have same topology
negative_passages.docid: 61220
negative_passages.text: What does "$\mathbb{F^n}$ is a vector space over $\mathbb{F}$" mean?
negative_passages.docid: 157109
negative_passages.text: Finding the Dimension of a Matrix Polynomial: $W$ = { $p(B)$ : $p$ is a polynomial with real coefficients}
negative_passages.docid: 100161
negative_passages.text: Is it true that $\dim(X) \leq \dim(X^{\ast})$ for every infinite dimentional Banach space $X$?