Geodesic
Structure of nilpotent matrices over fields
The electronic journal of linear algebra, Tome 22 (2011), pp. 931-958.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: A zero-nonzero pattern A is said to be potentially nilpotent over a field F if there exists a nilpotent matrix with entries in F having zero-nonzero pattern A. We explore the construction of potentially nilpotent patterns over a field. We present classes of patterns which are potentially nilpotent over a field F if and only if the field F contains certain roots of unity. We then introduce some sparse patterns of order n $\geq 4$ which are spectrally arbitrary over C but not over R. We also identify all irreducible patterns of order four which are potentially nilpotent over R or C.
Classification : 15A18, 05C05, 05C50, 15B35
Keywords: nonzero pattern, spectrum, potentially nilpotent, spectrally arbitrary, nilpotent- Jacobian method 
@article{ELA_2011__22__a16,
     author = {Campbell, Natalie and Vander Meulen, Kevin N. and Van Tuyl, Adam},
     title = {Structure of nilpotent matrices over fields},
     journal = {The electronic journal of linear algebra},
     pages = {931--958},
     publisher = {mathdoc},
     volume = {22},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2011__22__a16/}
}
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Campbell, Natalie; Vander Meulen, Kevin N.; Van Tuyl, Adam. Structure of nilpotent matrices over fields. The electronic journal of linear algebra, Tome 22 (2011), pp. 931-958. http://geodesic.mathdoc.fr/item/ELA_2011__22__a16/