Show that $T= \lambda I$, for some $\lambda \in F$, where $I$ is the identity map.
108012
A matrix $M$ that commutes with any matrix is of the form $M=\alpha I$
50037
Proving that kernels of evaluation maps are generated by the $x_i - a_i$
70304
Prove there are $\xi$, $\eta$ with $f'(\xi)f'(\eta)=1$
128457
Show that $T$ is a compact operator
101286
How show that $|a_{n}-1|\le c\lambda ^n,\lambda\in (0,1)$
118049
Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
143608
Show the Trace$(B)^{2} \leq$ nTrace$(B^{T}B)$
62303
For $V$ vector space of dimension $n$ under $\mathbb C$ and $T: V \to V $ linear transformation , show $V= \ker T^n \oplus $ Im $T^n$
28399
Showing $f$ is constant
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 $f(t)=c\cdot e^t$.
11322
Show that $f$ vanishes identically.
64650
If $a\operatorname{Re}(f(z))+b\operatorname{Im}(f(z))=c$ then f is constant
18379
Linear transformation $T:\mathbb{R}^{n}\rightarrow\mathbb{R}^{n}$ such that $T^{2}=\lambda T.$
67637
How come $\lambda(\mathbb{Q})= \inf\left\{\sum_{n \ge 1} \lambda([a_n,b_n)) : \mathbb{Q} \subset \bigcup_{n \ge 1} [a_n,b_n)\right\} = 0$?
80279
Show that $S + T$ and $aT$ are linear
65395
Prove that if $\operatorname{rank}(T) = \operatorname{rank}(T^2)$ then $R(T) \cap N(T) = \{0\}$
42809
How can we show that $(I-A)$ is invertible?