  Exceptional points~(EPs) appear as degeneracies in the spectrum of
non-Hermitian matrices at which the eigenvectors coalesce. In general, an EP of
order $n$ may find room to emerge if $2(n-1)$ real constraints are imposed. Our
results show that these constraints can be expressed in terms of the
determinant and traces of the non-Hermitian matrix. Our findings further reveal
that the total number of constraints may reduce in the presence of unitary and
antiunitary symmetries. Additionally, we draw generic conclusions for the
low-energy dispersion of the EPs. Based on our calculations, we show that in
odd dimensions the presence of sublattice or pseudo-chiral symmetry enforces
$n$th order EPs to disperse with the $(n-1)$th root. For two-, three- and
four-band systems, we explicitly present the constraints needed for the
occurrence of EPs in terms of system parameters and classify EPs based on their
low-energy dispersion relations.
