Proving either $T(v)=0$ or $T(x)=v$ has a solution for every $v$ in $V$?
112024
Let $T:V → V$ be a linear transformation where $V$ is finite dimensional.
76694
Proving that $UT=TU$ iff $U=g(T)$ for some polynomial $g$
133682
Prove that if $f(t)$ satisfies $f(t)=f'(t)$, then $f(t+s)=f(t)f(s)$ for all $t,s\in R$ without using the fact that $f(t)=c\cdot e^t$.
52928
If $\mathrm{Tr}(A)=0$ then $T=R^{-1}AR$ has all entries on its main diagonal equal to $0$
109228
Prove that $v, Tv, T^2v, ... , T^{m-1}v$ is linearly independent
103839
Proving that $T^{2} = T$ for a linear operator on $W$ implies that $V = \operatorname{Null} T \oplus \operatorname{Range} T$
100107
How can I prove that a linear map $T:V\to V$ such that $T^2 = I$ is equal to the Identity map?
81943
How to finish proof that $T$ has an infinite model?
24307
Is $x^x=y$ solvable for $x$?
85239
Proof $dim(W)=dim(V)=n \implies W=V$
35874
Show that when $BA = I$, the solution of $Ax=b$ is unique
65395
Prove that if $\operatorname{rank}(T) = \operatorname{rank}(T^2)$ then $R(T) \cap N(T) = \{0\}$
9143
Solve $u_{xx}-3u_{xt}-4u_{tt}=0$ where $u(x,0)=x^2$ and $u_t(x,0)=e^x$
100765
If $f'(x) = 0$ for all $x \in \mathbb{Q}$, is $f$ constant?
54217
Let $V$ be a vector space. Determine all linear transformations $T:V \rightarrow V$ such that $T=T^2$.
118873
Prove that $f(x)=0$ for all $x\in\mathbb{R}$.
138025
How to show the solution of $\dot{x} = Ax $ is an invariant subspace?