Show that there is a subspace $U$ of $V$ such that $V \cong U \oplus W$
4151
Every subspace of a vector space has a complement
28819
A union of two subspaces not equal to the vector space.
46746
How to prove if $u\in W^{1,p}$, then $|u|\in W^{1,p}$?
118049
Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
134065
A question about an $n$-dimensional subspace of $\mathbb{F}^{S}$.
121047
Proof: Sum of dimension of orthogonal complement and vector subspace
92774
Prove that a linear subspace of $C([0,1])$ is closed
131998
let ${v_1}, {v_2} $ be orthonormal basis for subspace $W$. Prove that if $z$ is a vector in $W$, then
11301
Union of two vector subspaces not a subspace?
41013
Subspace of $C^3$ that spanned by a set over C and over R
139988
Counter example for a result of intersection of subspaces
62077
Prove that if $W_1\subseteq V$ finite-dimensional, then there is $W_2\subseteq V$ such that $V=W_1\oplus W_2$
50159
How to prove if $\Bbb R^n=W_1\cup W_2\cup \cdots\cup $ where each $W_k$ is a subspace, then $\Bbb R^n=W_i$ holds for some $i$
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.
141794
Invariant subspaces of specific dimension
52135
Show that $A \setminus ( B \setminus C ) \equiv ( A \setminus B) \cup ( A \cap C )$
9854
If $U$ is a neighborhood of $e$, there exists $V$ neighborhood of $e$ such that $V^{-1}V \subseteq U$