Prove that there exists a natural number m such that each eigenvalue of A is an m-th root of unity
120933
A is similar to $A^k$, then each eigenvalue of $A$ is a root of unity
63183
Suppose $a,b,m,n$ are natural numbers, prove that if $a({m \over n})=b$ and $(a,n)=1$, then ${m \over n} \in \mathbb{N}$
127843
Prove that, for any natural number $k$ $\exists m \in M $ s.t i) $m$ has exactly $k$ $1$'s, an
31977
How to prove sum of powers property of roots of unity?
110086
Let $A$ be an $m \times n$ matrix. Show $A^TA$ and $AA^T$ have the same eigenvalues
31076
Roots of unity filter, identity involving $\sum_{k \ge 0} \binom{n}{3k}$
127056
How to prove that a polynomial of degree $n$ has at most $n$ roots?
153392
Let $A$ be a $n\times n$ matrix such that $a_{ij}=ij$,find the eigenvalues of the matrix $A$.
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?
86940
Proving an inequality in Eigenvalues of a matrix
67291
Prove that there exists $n\in\mathbb{N}$ such that $f^{(n)}$ has at least n+1 zeros on $(-1,1)$
126363
Are all algebraic integers with absolute value 1 roots of unity?
10001
Prove that the only eigenvalue of a nilpotent operator is 0?
39170
Existence of square root
128453
If $A$ has two eigenvalues $\lambda _1, \lambda_2$ and $\dim (E_{\lambda_1})=n-1$, then $A$ is diagonalizable
42165
Complex numbers and Roots of unity
107765
Prove that there exists two roots in $[-1,1]$