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Original Articles

Algorithms for Finding the Roots of Some Quadratic Octonion Equations

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Pages 3267-3282 | Received 01 Feb 2012, Published online: 04 Apr 2014

REFERENCES

  • Baez , J. C. ( 2002 ). The octonions . Bull. Amer. Math. Soc. 39 : 145 – 205 .
  • Dray , T. , Manogue , C. A. ( 1998 ). The octonionic eigenvalue problem . Adv. Appl. Clifford Algebras 8 : 341 – 364 .
  • Dray , T. , Manogue , C. A. ( 1998 ). Finding octonionic eigenvectors using Mathematica . Comput. Phys. Comm. ( 115 ): 536 – 547 .
  • Dray , T. , Manogue , C. A. , Okubo , S. ( 2002 ). Orthonormal eigenbases over the octonions . Algebras Groups Geom. 19 : 163 – 180 .
  • Dray , T. , Janesky , J. , Manogue , C. A. ( 2000 ). Some properties of 3 × 3 octonionic Hermitian matrices with non-real eigenvalues. Oregon State University, p. 12 .
  • Dray , T. , Janesky , J. , Manogue , C. A. ( 2000 ). Octonionic Hermitian matrices with non-real eigenvalues . Adv. Appl. Clifford Algebras 10 : 193 – 216 .
  • Farid , F. O. , Wang , Q. W. , Zhang , F. Z. ( 2011 ). On the eigenvalues of quaternion matrices . Linear Multilinear Algebra 59 ( 4 ): 451 – 473 .
  • Huang , L. , So , W. ( 2002 ). Quadratic formulas for quaternions . Applied Math Letters 15 : 533 – 540 .
  • Huang , L. , So , W. ( 2001 ). On left eigenvalues of a quaternionic matrix . Linear Algebra Appl. 323 : 105 – 116 .
  • Huang , Z. J. , Li , X. M. ( 2007 ). The theory of the roots for quadatic standard octonion equation . J. Guangzhou Radio and TV Univ. 7 : 44 – 63 .
  • von Neumann , J. P. , Wiger , J. ( 1934 ). On an algebraic generalization of the quantum mechanical formalism . Ann. Math. 35 : 29 – 64 .
  • Tian , Y. ( 2006 ). Matrix representations of octonions and their applications . Adv. Appl. Clifford Algebras 10 : 61 – 90 .
  • Tian , Y. ( 2010 ). Solving some linear equations over alternative rings . Results Math. 58 ( 3–4 ): 355 – 364 .
  • Zhang , F. Z. ( 1997 ). Quaternions and matrices of quaternions . Linear Algebra Appl. 251 : 21 – 57 .
  • Zhang , F. Z. ( 2007 ). Gersgorin type theorems for quaternionic matrices . Linear Algebra Appl. 424 : 139 – 153 .
  • Zhang , X. , Wang , Q. W. MATLAB: Octonion package, 2011 .
  • Communicated by J.-T. Yu.

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