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Results tagged with eigenvalues
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user 14094
eigenvalues of matrices or operators
7
votes
Accepted
Finite group is Dedekind iff for every irrep, every element acts as identity or has all eige...
The condition can be restated as: for every $g$ and $\rho$, the subspace $\mathrm{Ker}(\rho(g)-1)$ is a subrepresentation.
If $G$ is Dedekind (meaning that every subgroup is normal, or equivalently th …
- 63.9k
5
votes
Eigenvalues of positive matrices in $\mathrm{SL}(d,\mathbb{Z})$
3 (found by checking all $3\times 3$ matrices with entries in $\{1,2,3\}$): the matrix $\begin{pmatrix}1&1&1\\2&1&2\\2&3&1\end{pmatrix}$, with characteristic polynomial $x^3 - 3x^2 - 7x - 1$ has the eigenvalues … $$4.577...,\; -1.424...,\; -0.153...$$
Another one has only positive eigenvalues:
$\begin{pmatrix}3&1&1\\1&2&1\\2&1&1\end{pmatrix}$, with characteristic polynomial $x^3 - 6x^2 + 7x - 1$ with the eigenvalues …
- 63.9k