I was reading online when I came across this problem:
$$ A^2 = J + (k-1) I $$ where $A$ is a $n \times n$ square matrix where $n = k^2 - k + 1$, and $J$ is a matrix with all $1$s and $I$ is the identity matrix.
Is there a quick way from this expression to find the eigenvalues and eigenvectors for the square matrix?
