Given a subspace $W$ of $V$, does there always exist $\overline{W}$ such that $V = W\oplus \overline{W}$?
43504
Proving the existence of a complement subspace $U' \subset V$.
48579
How to find the orthogonal complement of a subspace?
123665
A question in Subspaces in linear algebra
78833
Can a basis for a vector space $V$ can be restricted to a basis for any subspace $W$?
143735
Prove/Disprove: For any sets $X$ and $Y$, $\overline{X\cap Y} = \bar{X}\cup\bar{Y}$
95379
Prove that $V = V_1 \oplus V_2$ in the following
99300
Prove if $W \subset V$ is a subspace such that $T(W)\subset W$, then $V/W$ is finite-dimensional.
141794
Invariant subspaces of specific dimension
105233
Is there a counterexample for the claim: if $A \oplus B\cong A\oplus C$ then $B\cong C$?
118049
Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
107842
Behaviour of ($\overline{a}_n)_{n=1}^{\infty}$ and ($\underline{a}_n)_{n=1}^{\infty}$
102168
Prove that there exists disjoint open subsets $U,V$ of $X$ such that $x \in U$ and $B \subseteq V$.
19396
For subspaces, if $N\subseteq M_1\cup\cdots\cup M_k$, then $N\subseteq M_i$ for some $i$?
63952
Disproving: If $(\Gamma\vdash(\phi\,\lor\psi))$, either $(\Gamma\vdash\phi)$ or $(\Gamma\vdash\psi)$ is true
92291
$U_1, U_2, ..., U_k$ subspaces of linear space $X$ with same dimensions, prove $X=U_1\oplus V=U_2\oplus V=...=U_k\oplus V$
76160
Dimension of the sum of two vector subspaces
81375
Why does $V(I(S))=\overline{S}$?