$V = U_1 \oplus W = U_2 \oplus W = \dots = U_k \oplus W$
92291
$U_1, U_2, ..., U_k$ subspaces of linear space $X$ with same dimensions, prove $X=U_1\oplus V=U_2\oplus V=...=U_k\oplus V$
121047
Proof: Sum of dimension of orthogonal complement and vector subspace
95206
If $\{u,v,w\}$ is a basis for $V$, then $\{u+v+w,v+w,w\}$ is also a basis: is this proof correct?
76694
Proving that $UT=TU$ iff $U=g(T)$ for some polynomial $g$
43504
Proving the existence of a complement subspace $U' \subset V$.
30583
If $a\mid b$ and $b\mid a$, $a,b\in R$, show that $\exists w \in R^\times$ with $b=wa$
89089
Prove that there is a unique inner product on $V$
151038
How to prove (A v B), (A → C), (B → D) therefore (C v D)
41520
Prove that $L(V,W)$ forms a vector space
15560
Prove that the union of three subspaces of $V$ is a subspace iff one of the subspaces contains the other two.
146339
Proof of -(-v)=v in a vector space
24128
How do i show that $w=z^2$ maps $|z-1|\leq 1$ onto $R=2(1+\cos \theta)$?
31069
Smallest and largest values of $\|\vec{v}-\vec{w}\|$
34147
$\|u\|\leq \|u+av\| \Longrightarrow \langle u,v\rangle=0$
14576
$(U\cap W)^0 = U^0 + W^0$
115295
Why are the two dot product definitions equal?
131609
Prove that $Au\cdot v = u\cdot A^Tv$