Top network posts

• 19 Prove that $\operatorname{SL}(n,\Bbb R)$ is connected.
• 13 Prove $(\mathfrak M^{-1})_S=(\mathfrak M_S)^{-1}$ and $(\mathfrak M \mathfrak N)^{-1}=\mathfrak M^{-1} \mathfrak N^{-1}$
• 12 $T$ be linear operator on $V$ by $T(B)=AB-BA$. Prove that if A is a nilpotent matrix, then $T$ is a nilpotent operator.
• 12 Prove that for any $n$, we have $\sum_{i=1}^n \frac{a_i}i \ge a_n $.
• 12 Check whether $f \mapsto f+ \frac{df}{dx}$ is injective or surjective
• 10 Is there an infinitely differentiable function such that $f$ intersects the $x$ axis only at the origin and no derivative of $f$ is $0$?
• 10 Explicit examples of cyclic groups which product is (non-)cyclic
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