ELA, Volume 16, pp. 30-43, January 2007, abstract.
Inertially arbitrary nonzero patterns of order 4
Michael S. Cavers and Kevin N. Vander Meulen
Inertially arbitrary nonzero patterns of order at most
4 are characterized. Some of these patterns are demonstrated
to be inertially arbitrary but not spectrally arbitrary.
The order 4 sign patterns which are inertially arbitrary
and have a nonzero pattern that is not spectrally arbitrary
are also described. There exists an irreducible nonzero
pattern which is inertially arbitrary but has no signing
that is inertially arbitrary. In fact, up to equivalence,
this pattern is unique among the irreducible order 4 patterns
with this property.