To prove that the dimension of $V$ is $d_1^2 + \ldots + d_k^2$
137890
Diagonalizable Operators and characteristic polynomials
49296
Prove $|(1+|u|^2)v-(1+|v|^2)u|>|u\bar{v}-\bar{u}v|$
145352
How to prove $\sum_{d|n} {\tau}^3(d)=\left(\sum_{d|n}{\tau}(d)\right)^2$
103854
Showing that $Q_n=D_n+D_{n-1}$
107520
Krull dimension of $\mathbb{C}[x_1, x_2, x_3, x_4]/\left$
59030
Finding the dimension of a given vector space
61539
proof for a basis in $L^2$
150720
Given that $W$ is a subspace of $V$, prove: $\dim W=\dim V \implies W=V$
55230
Dimension of set of commutable matrices
26780
Dimension of cone of projective variety
158170
vector space dimension of linear varieties
88728
Dimensions of vector subspaces in a direct sum are additive
115876
$D_6 \cong D_3\times \mathbb Z_2$
124786
Prove that V contains a subspace of each dimension
133087
Prove that, if $\{u,v,w\}$ is a basis for a vector space $V$, then so is $\{u+v, v+w, u+v+w\}$.
27478
Proof that two basis of a vector space have the same cardinality in the infinite-dimensional case
11665
Show that $D_{12}$ is isomorphic to $D_6\times C_2$