Prove subspace of finite dimensional vector space is finite dimensional
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.
69206
A finite-dimensional vector space cannot be covered by finitely many proper subspaces?
27478
Proof that two basis of a vector space have the same cardinality in the infinite-dimensional case
155621
Finiteness of the dimension of a normed space and compactness
124786
Prove that V contains a subspace of each dimension
134065
A question about an $n$-dimensional subspace of $\mathbb{F}^{S}$.
79061
show that {$(x_1,x_2,x_3,x_4)\in\mathbb{F}^4$:$x_3=5x_4+b$} is a subspace
92291
$U_1, U_2, ..., U_k$ subspaces of linear space $X$ with same dimensions, prove $X=U_1\oplus V=U_2\oplus V=...=U_k\oplus V$
41520
Prove that $L(V,W)$ forms a vector space
19415
Proof that every finite dimensional normed vector space is complete
95513
Proving $W$ is a subspace of $P_{2}$
70021
Verify if symmetric matrices form a subspace
15560
Prove that the union of three subspaces of $V$ is a subspace iff one of the subspaces contains the other two.
38516
Show a subset is subspace of a vectorspace and find the dimension
15300
How to show that $(W^\bot)^\bot=W$ (in a finite dimensional vector space)
76160
Dimension of the sum of two vector subspaces
51313
Extension of linearly independent set to a basis in an infinite dimensional vector space