M.H

 40 Do matrices $AB$ and $BA$ have the same minimal and characteristic polynomials? 27 Let $H$ be a subgroup of a group $G$ such that $x^2 \in H$ , $\forall x\in G$ . Prove that $H$ is a normal subgroup of $G$ 19 Evaluating the derivative of $\large \;e^{e^x}$? 18 First and second derivative of a summation 9 $AB-BA$ is a nilpotent matrix if it commutes with $A$

Reputation (10,588)

 +10 Do matrices $AB$ and $BA$ have the same minimal and characteristic polynomials? -2 Nilpotent blocks of matrices +10 First and second derivative of a summation +10 Let $H$ be a subgroup of a group $G$ such that $x^2 \in H$ , $\forall x\in G$ . Prove that $H$ is a normal subgroup of $G$

Questions (105)

 23 How to prove that $\frac{(5m)!(5n)!}{(m!)(n!)(3m+n)!(3n+m)!}$ is a natural number? 20 A group such that $a^m b^m = b^m a^m$ and $a^n b^n = b^n a^n$ ($m$, $n$ coprime) is abelian? 20 If $f''(x)+f(x)>0$ and $f(x)>0$ $\forall x\in(a,b)$; $f(a)=f(b)=0$; prove that $b-a>\pi$. 19 Maximal ideals in the ring of real functions on $[0,1]$ [closed] 19 How to compute the series $\sum\limits_{x=0}^\infty\sum\limits_{y=0}^\infty\sum\limits_{z=0}^\infty\frac{1}{2^x(2^{x+y}+2^{x+z}+2^{z+y})}$

Tags (111)

 103 calculus × 34 32 inequality × 16 92 linear-algebra × 50 30 integration × 24 76 matrices × 30 28 group-theory × 11 40 minimal-polynomials 28 summation × 8 40 characteristic-polynomial 27 abstract-algebra × 11

Bookmarks (453)

 1002 How long will it take Marie to saw another board into 3 pieces? 925 Can I use my powers for good? [closed] 756 The staircase paradox, or why $\pi\ne4$ 574 Why can you turn clothing right-side-out? 466 Is this Batman equation for real? [closed]