If every subspace of V is T-invariant, prove that T is a multiple of the identity map.
66283
Let V be a vector space. If every subspace of V is T-invariant, prove that there exist a scalar multiple c such that T=c1v
53261
Show that Pn is an (n+1)-dimensional subspace
144097
eigenvalues and eigenvectors of $vv^T$
143800
continuous map on $\mathbb{R}$ which is the identity on $\mathbb{Q}$ is the identity map, hence Aut$(\mathbb{R}/\mathbb{Q})= 1.$
73690
If $\mathbb R^3\setminus V$ connected where $V$ is the subspace generated by $\{(1,1,1),(0,1,1)\} $
20879
Let $T:V→V$ be a linear transformation satisfying $T^2(v)=-v$ for all $v\in V$. How can we show that $n$ is even?
15300
How to show that $(W^\bot)^\bot=W$ (in a finite dimensional vector space)
28565
Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$
102485
Showing that a topological space is ${\rm T}_1$
43504
Proving the existence of a complement subspace $U' \subset V$.
146143
Question about proof that finite-dimensional subspaces of normed vector spaces are direct summands
133087
Prove that, if $\{u,v,w\}$ is a basis for a vector space $V$, then so is $\{u+v, v+w, u+v+w\}$.
54217
Let $V$ be a vector space. Determine all linear transformations $T:V \rightarrow V$ such that $T=T^2$.
41520
Prove that $L(V,W)$ forms a vector space
141794
Invariant subspaces of specific dimension
73773
$C(M)=\{A\in M_n(\mathbb{C}) \mid AM=MA\}$ is a subspace of dimension at least $n$.
71064
How to prove that $\langle Av,w\rangle=\langle v,A^Tw\rangle$?