Every subspace $W$ of $F^n$ is the space of solutions of some system of homogeneous linear equations $AX=0$.
114906
For $n \in \mathbb{N}$ and $W \leq \mathbb{F}^n$, there exists a homogeneous system of linear equations whose solution space is $W$
33642
Finite dimensional subspace of $C([0,1])$
65494
Proper subspaces of $ R^n $
98949
Subspaces and annihilators
141674
Given $n$ linear functionals $f_k(x_1,\dotsc,x_n) = \sum_{j=1}^n (k-j)x_j$, what is the dimension of the subspace they annihilate?
73690
If $\mathbb R^3\setminus V$ connected where $V$ is the subspace generated by $\{(1,1,1),(0,1,1)\} $
4319
Vector space can be written as direct sum of subspaces
128835
Compactness of the set of $n \times n$ orthogonal matrices
134065
A question about an $n$-dimensional subspace of $\mathbb{F}^{S}$.
15560
Prove that the union of three subspaces of $V$ is a subspace iff one of the subspaces contains the other two.
150720
Given that $W$ is a subspace of $V$, prove: $\dim W=\dim V \implies W=V$
41611
Open and closed set in n by n matrices space.
139951
Direct Sum of vector subspaces
43504
Proving the existence of a complement subspace $U' \subset V$.
117575
Every proper subspace of a normed vector space has empty interior
86325
Is an increasing union of subspaces a subspace?
83337
If $A ∈M_n(C)$ is such that $(Ax,x) = 0$ for all $x ∈C^n$, then $A = 0$