If $a_n\to \ell $ then $\hat a_n\to \ell$
13701
Prove convergence of the sequence $(z_1+z_2+\cdots + z_n)/n$ of Cesaro means
359
Show that $\ker \hat{T} = \text{ann}(\text{range } T)$
96152
Showing that $a^n - 1 \mid a^m - 1 \iff n \mid m$
28565
Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$
62208
If $A$ is a non-empty set, then $A \notin A$
80009
Prove that $| |a|-|b| | \le |a-b|$
90525
The subspace of $\ell_2$
106584
If $A^{2n}=I$, then $A^n=\pm I$ where $A\in M_n(\mathbb{R})$
128305
$PGL(n, F)=PSL(n, F)$
150156
Proving that $S_n$ has order $n!$
19139
$T:\ell_2\to \ell_2, T(x_1,x_2,\dotsc)=(x_1,x_2/2,x_3/3,\dotsc)$
43246
Showing that if $a<b$, then $a^{1/n} < b^{1/n}$
95601
Is the multiplication operator on $\ell^p$ compact?
122580
If N is elementary nilpotent matrix, show that N Transpose is similar to N
59724
Proving that $x_n\to L$ implies $|x_n|\to |L|$, and what about the converse?
97656
Finding $a_n$ if $a_0=a_1=1,a_{n+1}=n(a_n+a_{n-1})\ \ (n\ge 1).$
17164
How do you show monotonicity of the $\ell^p$ norms?