Almost All Integer Matrices Have No Integer Eigenvalues
Greg Martin, Erick B. Wong · American Mathematical Monthly · 2009
In a recent issue of this MONTHLY, Hetzel, Liew, and Morrison [4] pose a rather natural question: what is the probability that a random n × n integer matrix is diagonalizable over the field of rational numbers? Since there is no uniform probability distribution on Z, we need to exercise some care in interpreting