Positive matrix with integer eigenvalues

Question

Is there any way of creating a positive matrix which has integer eigenvalues? Each entry $a_{ij}$ of the matrix must be strictly greater than $0$. I get how to create a matrix with certain eigenvalues using diagonal matrices, but I do not know how to make sure the matrix is strictly positive

Answer 1

The $n \times n$ matrix with diagonal entries $b$ and off-diagonal entries $a$ has eigenvalues $b-a$ (with multiplicity $n-1$) and $b + (n-1) a$.