Number of $k$-dimensional subspaces in $V$
15020
How to count number of bases and subspaces of a given dimension in a vector space over a finite field?
4319
Vector space can be written as direct sum of subspaces
125623
Subspaces of separable normed spaces
87692
Basis and dimension of vector space
37012
The number of summands $\phi(n)$
135814
Prove certain subsets of $\mathbb R^n$ are subspaces
107000
Dimension of intersection of distinct subspaces
6547
Given $3$-dimensional subspaces $V, W \subset \Bbb R^5$, there is a nonzero vector in $V \cap W$
43504
Proving the existence of a complement subspace $U' \subset V$.
4151
Every subspace of a vector space has a complement
73773
$C(M)=\{A\in M_n(\mathbb{C}) \mid AM=MA\}$ is a subspace of dimension at least $n$.
53633
Given two subspaces $U,W$ of vector space $V$, how to show that $\dim(U)+\dim(W)=\dim(U+W)+\dim(U\cap W)$
104578
Suppose that $V$ is a vector space, and $W$ is a subspace of $V$. If $V$ is finite dimensional, then prove $W$ too must be finite dimensional.
28402
Number of bases of an n-dimensional vector space over q-element field.
68006
Find the dimensions of some kernel subspaces of $\operatorname{Hom}(V, W)$.
19946
Let $W$ be a given subspace of $V$ find the orthogonal complement $W^{\perp}$
101993
The cardinality of a language over a set of variables $V$ with $\#V= κ$