1
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0answers
23 views

About the rank of (sub) matrices whose entries are roots of unity

Let $\Omega$ be a matrix with entries $a_{jk}=\omega^{jk}$, where $0\leq j,k\leq n-1$, and $\omega=e^{-2\pi i/N}$, with $N\in \mathbb{N}$, so $\Omega$ looks like $$ \Omega=\begin{pmatrix} 1 & 1 ...
1
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1answer
92 views

Conjecture about some group semiring representations ( and roots of unity ).

Let $\Bbb R_+=[0,\infty)$ be a semiring. $\Bbb R_+[C_n]$ is the group semiring formed by the semiring $\Bbb R_+$ and the cylic group $C_n$. Let $\Bbb R_+[X_n]$ be the polynomial semiring. ...
2
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3answers
254 views

3rd roots of unity as eigenvectors

Determine all eigenvalues of the matrix $$A=\begin{bmatrix}0&0&1\\1&0&0\\0&1&0\end{bmatrix}$$ and then determine a base for each eigenspace. It's easy to compute ...