New answers tagged linear-groups
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Eigenvalues of positive matrices in $\mathrm{SL}(d,\mathbb{Z})$
You are looking for Pisot matrices.
You may take a look at Avila and Delecroix - Some monoids of Pisot matrices.
5
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Eigenvalues of positive matrices in $\mathrm{SL}(d,\mathbb{Z})$
There is also in size 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 ...
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Eigenvalues of positive matrices in $\mathrm{SL}(d,\mathbb{Z})$
Did you look at any examples before asking the question?
I sat down to generate a positive integer matrix with determinant 1, and found this 4-by-4 example quickly:
$$\begin{pmatrix}1 & 2 & 3 &...
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