Geodesic
Inertially arbitrary nonzero patterns of order 4
The electronic journal of linear algebra, Tome 16 (2007), pp. 30-43.

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Summary: 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.
Classification : 15A18, 15A29, 05C50
Keywords: sign pattern, nonzero pattern, inertia, spectrum 
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     author = {Cavers, Michael S. and Vander Meulen, Kevin N.},
     title = {Inertially arbitrary nonzero patterns of order 4},
     journal = {The electronic journal of linear algebra},
     pages = {30--43},
     publisher = {mathdoc},
     volume = {16},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2007__16__a35/}
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Cavers, Michael S.; Vander Meulen, Kevin N. Inertially arbitrary nonzero patterns of order 4. The electronic journal of linear algebra, Tome 16 (2007), pp. 30-43. http://geodesic.mathdoc.fr/item/ELA_2007__16__a35/