query: If a vector subspace is in a union of other subspaces, then it's contained in one of them
positive_passages.docid: 19396
positive_passages.text: For subspaces, if $N\subseteq M_1\cup\cdots\cup M_k$, then $N\subseteq M_i$ for some $i$?
negative_passages.docid: 74465
negative_passages.text: One-dimensional vector space and it's subspaces
negative_passages.docid: 78833
negative_passages.text: Can a basis for a vector space $V$ can be restricted to a basis for any subspace $W$?
negative_passages.docid: 86325
negative_passages.text: Is an increasing union of subspaces a subspace?
negative_passages.docid: 121047
negative_passages.text: Proof: Sum of dimension of orthogonal complement and vector subspace
negative_passages.docid: 44431
negative_passages.text: The dimension of a subspace is less than dimension of the whole space.
negative_passages.docid: 41347
negative_passages.text: The dimension of the intersection of two vector subspaces
negative_passages.docid: 18572
negative_passages.text: Union of a family of connected pairwise not disjoint subspaces is connected
negative_passages.docid: 53261
negative_passages.text: Show that Pn is an (n+1)-dimensional subspace
negative_passages.docid: 43504
negative_passages.text: Proving the existence of a complement subspace $U' \subset V$.
negative_passages.docid: 107000
negative_passages.text: Dimension of intersection of distinct subspaces
negative_passages.docid: 74623
negative_passages.text: Associative rule of subspaces and vector spaces: $(U+V) \cap W = U + (V \cap W)$
negative_passages.docid: 28819
negative_passages.text: A union of two subspaces not equal to the vector space.
negative_passages.docid: 33642
negative_passages.text: Finite dimensional subspace of $C([0,1])$
negative_passages.docid: 45111
negative_passages.text: Number of Subspaces that contains other Space
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: 1799
negative_passages.text: How many k-dimensional subspaces there are in n-dimensional vector space over $\mathbb F_p$?