@article {IOPORT.06098831,
    author       = {Campbell, Natalie and Vander Meulen, Kevin N. and Van Tuyl, Adam},
    title        = {Structure of nilpotent matrices over fields.},
    year         = {2011},
    journal      = {ELA. The Electronic Journal of Linear Algebra [electronic only]},
    volume       = {22},
    issn         = {1081-3810},
    pages        = {931-958, electronic only},
    publisher    = {ILAS - The International Linear Algebra Society c/o Daniel Hershkowitz, Department of Mathematics, Technion - Israel Institute of Techonolgy, Haifa},
    abstract     = {Summary: A zero-nonzero pattern $A$ is said to be potentially nilpotent over a field $\Bbb F$ if there exists a nilpotent matrix with entries in $\Bbb F$ 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 $\Bbb F$ if and only if the field $\Bbb F$ contains certain roots of unity. We then introduce some sparse patterns of order n $\geq 4$ which are spectrally arbitrary over $\Bbb C$ but not over $\Bbb R$. We also identify all irreducible patterns of order four which are potentially nilpotent over $\Bbb R$ or $\Bbb C$.},
    identifier   = {06098831},
}