Prove that $\{v_1, v_2, n\}$ is a basis
3543
Prove set is basis for $R^3$
53633
Given two subspaces $U,W$ of vector space $V$, how to show that $\dim(U)+\dim(W)=\dim(U+W)+\dim(U\cap W)$
79061
show that {$(x_1,x_2,x_3,x_4)\in\mathbb{F}^4$:$x_3=5x_4+b$} is a subspace
146690
Basis for adjoint representation of $sl(2,F)$
92291
$U_1, U_2, ..., U_k$ subspaces of linear space $X$ with same dimensions, prove $X=U_1\oplus V=U_2\oplus V=...=U_k\oplus V$
132487
Proving that if $V$ is an inner product space and $U_1, U_2$ are subsets, then $U_1 \subset U_2$ if and only if $U^{\perp}_2 \subset U^{\perp}_1$
62077
Prove that if $W_1\subseteq V$ finite-dimensional, then there is $W_2\subseteq V$ such that $V=W_1\oplus W_2$
27564
Prove that $\|UVU^{-1}V^{-1}-I\|\leq 2\|U-I\|\|V-I\|$
112939
Find a basis for the subspace of $\mathbb{R}^4$ spanned by the given vectors.
27478
Proof that two basis of a vector space have the same cardinality in the infinite-dimensional case
100257
Converse to Hilbert basis theorem
123275
Prove $[A,B^n] = nB^{n-1}[A,B]$
70475
Proving a basis for inner product space V when $||e_j-v_j||< \frac{1}{\sqrt{n}}$.
38412
Basis for tensor products
76188
Show $(W_1 + W_2 )^\perp = W_1^\perp \cap W_2^\perp$ and $W_1^\perp + W_2^\perp ⊆ (W_1 \cap W_2 )^\perp$
83116
Uncountability of basis of $\mathbb R^{\mathbb N}$
116908
Basis for set of nxn matrices with trace = 0