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Linear and Multilinear Algebra Volume 60, 2012 - Issue 1
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Original Articles

Complex spectrally arbitrary zero–nonzero patterns

J.J. McDonald Department of Mathematics, Washington State University, Pullman, WA 99164, USACorrespondence[email protected]
&
A.A. Yielding Department of Mathematics, Eastern Oregon University, La Grande, OR 97850, USA
Pages 11-26 | Received 23 May 2008, Accepted 15 Jul 2010, Published online: 25 Aug 2011

References

  • Britz , T , McDonald , JJ , Olesky , DD and van den Driessche , P . 2004 . Minimal spectrally arbitrary sign patterns . SIAM J. Matrix Anal. Appl. , 26 : 257 – 271 .
  • Cavers , MS and Vander Meulen , KN . 2005 . Spectrally and inertially arbitrary sign patterns . Linear Algebra Appl. , 394 : 53 – 72 .
  • Cavers , MS and Vander Meulen , KN . 2007 . Inertially arbitrary nonzero patterns of order 4 . Electron. J. Linear Algebra , 16 : 30 – 43 . (electronic)
  • Corpuz , L and McDonald , JJ . 2007 . Spectrally Arbitrary Zero-Nonzero Patterns of Order 4 . Linear Multilinear Algebra , 55 : 249 – 273 .
  • DeAlba , LM , Hentzel , IR , Hogben , L , McDonald , JJ , Mikkelson , R , Pryporova , O , Shader , B and Vander Meulen , KN . 2007 . Spectrally arbitrary patterns: Reducibility and the 2n conjecture for n = 5 . Linear Algebra Appl. , 423 : 262 – 276 .
  • Drew , JH , Johnson , CR , Olesky , DD and van den Driessche , P . 2000 . Spectrally arbitrary patterns . Linear Algebra Appl. , 308 : 121 – 137 .
  • Farahat , HK and Ledermann , W . 1958/1959 . Matrices with prescribed characteristic polynomials . Proc. Edinb. Math. Soc. , 11 : 143 – 146 .
  • Friedland , S . 1972 . Matrices with prescribed off-diagonal elements . Israel J. Math. , 11 : 184 – 189 .
  • Kim , IJ , McDonald , JJ , Olesky , DD and van den Driessche , P . 2007 . Intertias of zero–nonzero patterns . Linear and Multilinear Algebra , 55 : 229 – 238 .
  • Kim , IJ , Olesky , DD and van den Driessche , P . 2007 . Inertially arbitrary sign patterns with no nilpotent realization . Linear Algebra Appl. , 421 : 264 – 283 .
  • Kirkland , SJ , McDonald , JJ and Tsatsomeros , MJ . 1996 . Sign Patterns which require a positive eigenvalue . Linear Multilinear Algebra , 41 : 199 – 210 .
  • MacGillivray , G , Tifenbach , RM and van den Driessche , P . 2005 . Spectrally arbitrary star sign patterns . Linear Algebra Appl. , 400 : 99 – 119 .
  • McDonald , JJ , Olesky , DD , Tsatsomeros , MJ and van den Driessche , P . 2003 . On the spectra of striped sign patterns . Linear and Multilinear Algebra , 51 : 39 – 48 .
  • McDonald , JJ and Stuart , J . 2008 . Spectrally arbitrary ray patterns . Linear Algebra Appl. , 429 : 727 – 734 .
  • Shader , BL . ‘Notes on the 2n conjecture’. From American Institute of Mathematics workshop: Spectra of families of matrices described by graphs, digraphs, and sign patterns, 2008. Available at http://www.aimath.org/pastworkshops/matrixspectrum.html♯2nSAP
  • Yeh , L . 1996 . Sign pattern matrices that allow a nilpotent matrix . Bull. Aust. Math. Soc. , 53 : 189 – 196 .

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