$\operatorname{rank}(g\circ f)\le \min\{\operatorname{rank}(f), \operatorname{rank}(g)\}$ proof?
121264
Prove that rank $(g \circ f)\le \min[\operatorname{rank}(f),\operatorname{rank}(g)]$; $g$ and $f$ are linear mappings
42266
Show that $d(x,y)=\min \{1,|x-y|\}$ is a metric on $\mathbb R$
145339
Index of the subgroup $\operatorname{Im}(f)$
93806
$\|f\|_{L^{p}}=\sup\left\{\int_{{\bf R}^{n}}|f(x)g(x)|~dx:\|g\|_{L^{q}}\le1\right\}$
101371
show that $f^{(3)}(c) \ge 3$ for $c\in(-1,1)$
71040
If $ \operatorname{Tr}(M^k) = \operatorname{Tr}(N^k)\;\forall 1\leq k \leq n$, then how do we show the $M$ and $N$ have the same eigenvalues?
36099
Show that $\|f\|^{2}$ attains a minimum value on the interior of $B$
28658
$R$ with an upper bound for degrees of irreducibles in $R[x]$
130537
Proving that $d(f,g)=\|f-g\| = \sup \limits_{0\leq x \leq 1} |f(x)-g(x)|$ is a metric on $X=C[0,1]$
131212
Prove that if $A$ is regular then $\operatorname{adj}(\operatorname{adj}(A)) = (\det A)^{n-2} A$
136909
Functional Analysis: The rank of an operator detemines if it's a compact operator.
7890
Prove the map $\Phi:G\to\operatorname{Aut}G$ with $g\mapsto (x\mapsto g^{-1}xg)$ is an homomorphism.
138069
Proof that $\bigcap_{a\in A} \bigg(\, \bigcup_{b\in B} F_{a,b} \, \bigg) = \bigcup_{f\in ^AB} \bigg(\, \bigcap_{a \in A} F_{a,f(a)}\,\bigg) $
98816
How to prove that $\{f+g<a\}=\bigcup_{r\in{\Bbb Q}}(\{f<r\}\cap\{g<a-r\})$?
147014
Matrix algebra: If $A^2=0$, Proof rank(A) $\le \frac{n}{2}$
105910
How to prove that $[G:xHx^{-1}] = [G:H]$ given $H \le G$?
106101
Why there is much interest in the study of $\operatorname{Gal}\left(\overline{\mathbb Q}/\mathbb Q\right)$?