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Linear and Multilinear Algebra Volume 60, 2012 - Issue 3
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Original Articles

Spectrally arbitrary patterns over finite fields

E.J. Bodine Department of Mathematics, Cabrini College, Radnor, PA, USA
&
J.J. McDonald Department of Mathematics, Washington State University, Pullman, WA, USACorrespondence[email protected]
Pages 285-299 | Received 15 Mar 2011, Accepted 22 May 2011, Published online: 25 Aug 2011

References

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  • Brualdi , RA , Hogben , L and Shader , BL . AIM Workshop: Spectra of families of matrices described by graphs, digraphs and sign patterns . Final Report: Mathematical Results , 30 March 2007. Available at: http://aimath.org/pastworkshops/matrixspectrumrep.pdf
  • Catral , M , Olesky , DD and van den Driessche , P . 2009 . Allow problems concerning spectral properties of sign pattern matrices: A survey . Linear Algebra Appl. , 430 : 3080 – 3094 .
  • Cavers , MS and Vander Meulen , KN . 2005 . Spectrally and inertially arbitrary sign patterns . Linear Algebra Appl. , 394 : 53 – 72 .
  • Corpuz , L and McDonald , JJ . 2007 . Spectrally arbitrary zero–nonzero patterns of order 4 . Linear Multilinear Alg. , 55 : 249 – 273 .
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  • MacGillivray , G , Tifenbach , RM and van den Driessche , P . 2005 . Spectrally arbitrary star sign patterns . Linear Algebra Appl. , 400 : 99 – 119 .
  • McDonald , JJ and Stuart , J . 2008 . Spectrally arbitrary ray patterns . Linear Algebra Appl. , 429 : 727 – 734 .
  • McDonald , JJ and Yielding , AA . 2011 . Complex spectrally arbitrary zero–nonzero patterns whose Jacobian are zero at every nilpotent realization . Linear Algebra Multilinear Algebra , published on iFirst 26 August 2011
  • Niven , I , Zuckerman , HS and Montgomery , HL . 1991 . An Introduction to the Theory of Numbers, , 5th , New York : Wiley .
  • Vander Meulen , K and Van Tuyl , A . 2009 . Zero–nonzero patterns for nilpotent matrices over finite fields . Electronic J. Linear Algebra , 18 : 628 – 648 .

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