### Questions (226)

 16 easier way of calculating the determinant for this matrix 15 Prove/disprove: if $\det(A+X) = \det(B + X)$ for all $X$, then $A=B$ 14 Proving that $\frac{(k!)!}{k!^{(k-1)!}}$ is an integer 9 Proving that $\sum\limits_{k=0}^{n} {{m+k} \choose{m}} = { m+n+1 \choose m+1 }$ [duplicate] 9 Prove that in a tree with maximum degree $k$, there are at least $k$ leafs

### Reputation (4,535)

 +10 Show that $\sum_{n=1}^{\infty} {(-1)^n \sin(\frac{x}{n})}$ converges for $a > 0$ in $[-a,a]$ +10 Solving linear equations with Vandermonde +10 Prove: If in all subgraphs of $G$ there is a vertex of degree $<2$ then $G$ is a forest +10 SVD of a $3 \times 2$ matrix

 4 If $L_2L_1$ is accepted by a DFA, is $L_1$ too? 2 Prove that in two trees with same vertices there exists a vertex that the sum of its' degree in both trees is maximum $3$ 1 Are cyclic groups always abelian? 0 $(X,\sqrt{|i-j|)}$ is Euclidian 0 Throwing of non-fair dice

### Tags (75)

 4 automata × 8 1 abelian-groups × 2 4 finite-automata × 2 1 intuition 2 graph-theory × 26 1 cyclic-groups 1 abstract-algebra × 22 0 linear-algebra × 47 1 group-theory × 8 0 calculus × 40