A matrix
$A$
with minimum polynomial
$m_A$
and characteristic polynomial
$c_A$
is said to be cyclic if
$m_A = c_A$
, semisimple if
$m_A$
has no repeated factors, and separable if it is both cyclic and semisimple. For any set
$T$
of matrices, we write
$C_T$
for the proportion of cyclic matrices in
$T, SS_T$
for the proportion of semisimple matrices, and
$S_T$
for the proportion of separable matrices. We will write
$C_{{\rm GL}(\infty,q)}$
for
$\lim_{d\rightarrow\infty}C_{{\rm GL}(d,q)}$
, and so on.